I'm thinking of doing a milare run to BOM. The BA flight arrives at 12:15 am and the return flight is at 2:15 am.

Will I need to clear immigation & customs and reenter the building?

How does one transit BOM?

Is 2 Hours enough?

you're doing a mileage run to BOM? From where? what kind of fare did you pay?

have no idea about the immigration situation, but you'll probably have to be a "transit" passenger of some sort-- if you actually have to go out of immigration and come back in, you're unlikely to make it in time.

I am making a milage run...

ORD to LHR
LHR to BOM
BOM to LHR
LHR - ORD

It's also a working trip for me, as I can get a lot done on airplanes, given the uninterrupted time away from the kids.

In BOM you can transit. Just don't follow the crowd and look for a yellow 'transit' sign. You will have to redo security.

You will be questioned about your entering the transit zone and you will need to show a ticket or BP. You should have a BP already when you land. There is no BA counter airside.

Most mortals from any country in the world need a visa to enter India. So if the airside transit is not possible if you don't get your return BP in LHR, you need to get a visa ahead of time in the country where you normally reside. Then you also need to leave the airside, pass thru immigration (45-60mins), checkin upstairs (10-15mins) and re-enter thru immigration (45-60min).

Indian immigration officers are a kind bunch to non-indians. But I seriously doubt you can explain a MR to an indian immigration officer in BOM. He WILL notice you just came into the country since your passport will be stamped and you have to submit the landing card you receive when entering the country. Most officers in BOM are maratha PSI coming from the surrounding countryside. An intercontinental trip is something some of them never will do. Your 'story' will be severly doubted.

Summary: either you stay atleast 1day in BOM or look for a non-indian destination to do your MR!