Ok, Tourist visa is not B1, B1 is a business visa.
You cannot train, study or work on a tourist visa.
In any event, a business visa is ONLY appropriate if you are an employed current commercial pilot, going for recertification or to maintain an existing rating, and there is no classroom work.
The above is from the US Embassy in London.
If you are going for an initial which involves licence issue, which it sounds like you are, you will need an M1 student Visa
I'm going for a type rating on my JAA ATPL, and to use the checkride for the issue of the FAA ATP. I'm getting an M1 because it's a new type rating, and I'm getting a licence issued in the US.
I know many people go on business or even the visa waiver programme. My understanding is that this is *technically* innapropriate if you are going to obtain a licence (ie. not revalidate or maintain something you already have, or have had).
Most get away with it it appears, but I don't want a paper trail in the US that someone could use to figure out I took flight training illegally in the US at some point in the future, even if I do make it in and out without being stopped.