The movement has three phases, those being:
Nashville to the Duck river
Bridging the Duck
Duck river to Shiloh
Of these:
To the Duck
The map I've looked at shows Buell leaving Nashville on 16 March, which accords with Ammen's bde leaving on the 17th and not being the leading brigade of the movement. Here to the Duck is a march of 43 miles, so we'd expect Buell to arrive here around the 20th or so if he's moving at around 10 miles per day, and indeed McCook is repairing the bridges by the 20th (Ammen's account).
Bridging the Duck
The destruction of the bridges and the ford being unmanageably high is the main cause of the delay here. If the bridge had been completely undestroyed and the divisions could just march through, then we'd expect Buell's head of column to have arrived at Shiloh (with a march rate of 10 miles per day) around the 30th (which would put him having marches on the 16th-30th inclusive, 15 days, to travel about 143 miles).
Instead, his divisions arrive about a week after that (leading division arrives on the 6th April).
Duck river to Shiloh
On this stage, Buell actually "makes up" time compared to what we would expect.
Thus, in both the cases where Buell's army is in motion, it's moving as we would expect if not faster.
This implies to me that the big concern is bridging the Duck river, and that that cost about a week compared to an "optimal route march" at 10 miles a day for the whole distance. It doesn't seem unreasonable to me, especially when he has no dedicated engineers and is trying to bridge a flooded river.