This shouldn't in fact be too hard. Note that, despite what is sometimes said, officers did transfer between battalions of the same BNI regiment, certainly in this period.

First call should be Hodson's "Officers of the Bengal Army"; this should have an entry for your chap. Sometimes it doesn't contain information on the battalion, but it normally does. Also, where he served with them will often give it away.

Second call, if Hodson isn't helpful, is the "Bengal Military Accounts", which are summarised annually, and are available from the Oriental and India Office Collection at the British Library. The 1812 Accounts, for example, reflect back on 1811. If you are interested in a particular year, each battalion and regiment has their own pages, containing the life of the regiment, at least in terms of arrivals, departures, transfers etc., in detail.

I hope that helps.

George