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.