I have purchased a number of BB MTM suits. There are essentially two options: the 1818 line which is half canvas construction (floating chest piece) and made in their MA factory and the Golden Fleece line which is full canvas construction and made in their NY factory. Which you select is dependent on two things: how much you want to spend and what fabric you choose (certain fabrics are for one line and not the other).
In general, with both options, they will take a fairly comprehensive series of measurements and then discuss the pattern style (Fitzgerald versus Madison, etc.). The results are usually very good, but expect that you will need at least two rounds of adjustments with the local in-store tailor once your suit comes in.
Make sure you use the same tailor at each step otherwise things can go terribly wrong.
Have a good idea of what style suit you are looking for; they can make just about anything you could want, but walking in without a concept in mind can end with a mess of a suit and a lot of unwanted doodads and associated costs.
Take the time to pick the fabric you want (color, weight, etc.).
Be prepared for the whole measuring, fabric selection process and ordering to take at least 90 minutes to 2 hours.
Expect to pay ~ 2000 dollars for a 3 piece MTM if half canvas, ~ 3000+ for 3 piece if full canvas + "Saxxon" wool, etc. (that is with various discounts you undoubtedly be offered - don't keel over when the initial numbers come in higher).
Let the salesman talk you into things you don't want.
Fail to spend enough time with the tailor; he should be your sounding board and guide, not the salesman.
Focus on anything else but the MTM process on that particular visit to the store.
Let them put buttons, button holes, etc. at the factory; have them prep for details but let the store tailor finalize those items (I don't know if this is an option everywhere, or just in NY).
I have had good experiences with the BB MTM process at their NY store and have been very happy with the suits produced (they are much better today than during their ownership under Marks & Spencer). There is, IMHO, no comparison between the BB MTM suits versus their OTR counterparts; even if line-labels (1818, Golden Fleece, etc.) are the same, the MTM stuff is worlds better (and you pay for it ).