Since you are not looking for a computer analysis, I would say that just looking at it, I would have taken with the bishop since it would be well-placed on d4 and gained a tempo. Then moved the king closer to d3. This would have rendered all of black's counterplay harmless.
I would have tried to avoid exchanging on c4 if at all possible, but even if not, with the king on d3, dxc4+ Kc3 would really stop b4 for a long time since then you would be pushing would lose the newly-created c4-pawn.
a4 was definitely a huge mistake giving black two passers. If it is not already lost there, it was probably at least equal already...so avoid a4 unless there is a very good reason since you do not want to give your opponent passed pawns that are that well supported.