We share a transformer with another company who has the B-Leg grounded on a Wye system as opposed to a center tap ground. By doing this it acts very similarly to a Delta system. Does it act similar enough to a Delta system to do a study as if it were a Delta or is there a better approach?

Yes you could model this as a delta with a B-phase ground. You could add a +30deg phase shift to make it a bit more accurate. The easiest way to look at this is draw a wye with A-phase at 0 degrees, then form a triangle around the wye. You will see the A-B line is at 30 degrees (either negative or positive based on rotation)

I would be concerned about two different points of grounding. A "Y" connected secondary are grounded at the common point to the three windings, the corner ground or "B" phase grounded have one phase conductor grounded. If you get between the two grounds, there is 277 volts. So if there are conductive objects between the two locations someone may get surprised.

If you are doing an arc flash study it does not matter, it is a delta system

Actually, I wouldn't think you would have both the center and the 'B' phase bonded to ground. If you are going to bond the 'B' phase to ground, I would think you should let the center tap float

You cannot bond both to ground, you will have a short circuit - what am I missing?