Buell's [slow] March from Nashville to Savannah, Tennessee
It all began when C.F. Smith's expedition up the Tennessee River to destroy Confederate railroad lines was converted into an offensive operation, involving overwhelming force, to take place at Corinth, Mississippi. And General Don Carlos Buell commenced his march out of Nashville about March 15th to join his Army of the Ohio with Grant's Army of the Tennessee (and it was understood -- by Buell -- that this combined Army would be led south against Corinth by General Halleck, in person... once "that other business keeping him in St. Louis" was completed.)
And Buell also understood that a major component of his trek south and west revolved around the rebuilding of bridges (as necessary), and the extension of a telegraph line from Nashville to Savannah [OR 11 page 43: March 17th 1862, Halleck to Buell.]
The lack of urgency in completing the transit was further imparted by U.S. Grant, as late as April 4th, when Buell received a courier-delivered message from Grant, advising Buell, "Do not hasten, because I can not put you across the river until Tuesday [April 8th]" (from Buell's Shiloh Reviewed, page 491.)
Luckily (for Federal supporters), General William "Bull" Nelson sensed urgency and sought permission to ford the Duck River before the "official opening" of the rebuilt Duck River Bridge, end of March. This "hasty movement" not only ensured Nelson's Division arrived at Savannah at Noon on April 5th; but Nelson passing beyond Waynesborough put paid to a request by Buell to use Waynesboro "as a base" while awaiting Halleck's arrival at Savannah/Pittsburg [OR 11 page 94.]
According to Colonel Jacob Ammen's Diary [found in OR 10 beginning page 331], upon his arrival at Savannah on April 5th, he immediately reported to U.S. Grant's Headquarters at the Cherry Mansion, but failed to find General Grant. Ammen directed his 10th Brigade south and west of Savannah, about a half to three-quarters of a mile from Grant's HQ, and set up camp. At about 3pm General Grant appeared, in company with General Bull Nelson, at Ammen's camp. The conversation included Grant telling Ammen, "You cannot march through the swamp [to approach Pittsburg Landing]" and "I will send boats for you on Monday or Tuesday [to take your brigade from Savannah to Pittsburg Landing.]" Grant rode away, in company with General Nelson. And General Buell showed up at Ammen's HQ tent about sundown on April 5th. [But Buell did not announce his arrival to U.S. Grant.] However, it appears a meeting was scheduled to take place, Grant and Buell, at the Cherry Mansion, next morning.
Early Sunday morning, Jacob Ammen was up preparing for the inspection and parade of his brigade, which he'd scheduled for 9am. While eating breakfast, the sound of scattered firing, growing ever louder, more intense, came from the southwest. Becoming certain that a battle was taking place in vicinity of Pittsburg Landing, Colonel Ammen sent a party of men [not identified, but likely cavalrymen] south and west down the road, to determine if it was possible to march infantry through to the riverbank opposite Pittsburg Landing. Ammen cancelled the inspection; changed focus of his 10th Brigade to "preparing for battle" (and during this preparation, Bull Nelson appeared, and directed him to "Be ready," and then advised that he was "on his way to Savannah, to watch for boats."
When Colonel Ammen fronted up to the Cherry Mansion for orders [at about 9am by my estimate], Buell and Nelson were already there. But, General Grant and his staff were not there, having all departed aboard Tigress before Buell arrived [my estimate, Buell arrived at Cherry Mansion between 8- 8:30 and missed Grant by as little as fifteen minutes.] It was assumed that General Grant would send steamers to Savannah [based on earlier conversations]. And although U.S. Grant claims that he left a message, directing Nelson to "march through the swamp," Nelson claims that he never received that message. Meanwhile, there being no steamers at Savannah, Buell, Nelson and Ammen decided to wait... especially after the first member of Ammen's reconnaissance party reported at the Cherry Mansion, with "unfavorable details" in regard to "getting through the swamp."
While waiting, Jacob Ammen discovered that his old friend from West Point, Charles Smith (now Major General Smith) was upstairs in the Cherry Mansion, recovering from a leg injury. Ammen went up and chatted with Smith for an extended period... until Ammen was called outside by an orderly; and returned to the yard to interview the other troopers, just returned from scouting the swamp. Their report: "they could not find a way through." Worse news: there were still no boats at Savannah.
About noon, a small steamer was seen approaching Savannah, from the north. Before flagging it down, and departing on that steamer, General Buell directed Nelson to, "March through the swamp at 1pm, if no transport has arrived by then." (Between the report of "no way through the swamp," and Buell's departure, a man described by Ammen as "a tall Tennessean" appeared on the scene, and announced, "he was a strong Union man, and he could guide men across that swamp, but not wagons or artillery."
It appears Buell departed Savannah in company with his Chief of Staff at about 1pm. [He arrived at Pittsburg Landing just before 2pm, and met a steamer bearing a message for him from General Grant, along the way.] No other transport arrived at Savannah; Ammen records in his diary that the 10th Brigade commenced its march at 1pm; (and Bull Nelson recorded in OR 10 page 323 the start of that march at 1:30.) Ammen further records that "they started on a good road that ran along a ridge, for about three miles. Then, the guide led them down, into the black-mud swamp." After struggling through for a few minutes, Ammen asked, "How much farther?" To which, the guide replied, "Only five miles more, through this swamp, to the landing." As they pressed on, Ammen recalls crossing a sturdy bridge -- securely fastened down -- that spanned a water-filled ditch, and then returning to the endless mud. Eventually, sparse timber gave way to dense forest; but the mud and ankle-deep water persisted. Ammen recorded, as he looked down, and peered through the flooded forest, "that if there is a road, the high water has erased its trace." With two miles to go, General Nelson, in company with a cavalry company, came splashing up, commended Ammen on his progress, and galloped ahead... after taking possession of Ammen's guide. "It was actually easier," says Ammen, "to follow the trail left by a hundred horses." And the sound of battle, coming from their front, boomed and crackled, unabated; only now, men's shouts punctuated the metallic thunder.
Finally, after slipping and sloshing four hours, Jacob Ammen emerged from the forest, onto a field that bordered the Tennessee River. A path was quickly hacked into the steep bank, leading down to the river, to facilitate loading of men and horses; the job finished just before the first steamer arrived. But even with the arrival of the boats, there was a problem: every steamer arrived already crowded with wounded men and stragglers. Only about four companies of Army of the Ohio troops could be crammed aboard each steamer. Still, the first fresh troops of that Army stepped ashore at Pittsburg Landing, just after 5:30 pm [OR 10 page 339.]
To find out more, have a look at some of the linked references...
References: OR 10 (pages as indicated, especially page 331 -- Ammen's Diary)
OR 11 pages 11, 43, 44 and 94
http://www.aotc.net/Shiloh.htm#Buell Shiloh Reviewed, by D.C. Buell (1885)