I have done this almost monthly for the past 5 months.

The bus from T1 to T2 is hopelessly slow, although arguably easier than what I do.

I take the transit train from T1 to T2 which takes about 8 minutes, and it is then a 12-15 minute walk from the stop at T2 to the BA desks.

Personally I would recommend the train, although I appreciate with baggage it can be a hassle.

3 hours is more than enough.