See, you can look at that recipe transcribed from Beersmith and tell the calculations are messed up. Batch size is 5.5 gallons, but the post-boil volume shown is 6.24 gallons. I am willing to wager you don't have 3/4 gallons of trub or other losses going into the fermenter.
I am not sure what your boil-off rate is, but I'm going to assume it is like mine and you boil off about 1 gallon per hour.
If you are using 13.8 lbs of grain, and you squeeze the bag after you pull it out, you want a total volume of around:
5.5 + 1.0 (for boil-off) + 1.4 (for grain absorption) = 7.9 gallons of water
If you do a full volume BIAB mash, your total volume in the pot, including the grain, would be a bit under 9 gallons total in the pot.
Here is a link to the calculator I wrote. There is also a calculator for sizing a regular MLT for 2- or 3-vessel brewing.
Google docs sizing spreadsheet
Again, the calculator assumes that you are using the full volume all in the same pot. If you want to dunk sparge in a different pot, or add the sparge water later, then use the same total volume, but put part of it in the other vessel. For a regular MLT I typically use 1.5 quarts/lb for the mash, which in your case is going to be approximately 5 gallons.
Also,
DO NOT use the strike water temperatures indicated in Beersmith, as they are woefully wrong. Heat your strike water up to about 2 degrees higher than your target mash temp, and thoroughly stir in your grain. If you are a bit low, gently(!) heat your pot while stirring (be sure to transfer mass from the bottom to the top, not just side-to-side) until you are at the target mash temp. If you are high, stir until it cools down to the target.
Dont have time to dig to much into it now but I think it's in the Water Vols tab, kettle top up maybe???
