Last time I had to stay in Bayswater, actually a nice little, very reasonable hotel http://www.queensparkhotel.com I used the Heathrow Express https://www.heathrowexpress.com/ and then jumped in a tube at Paddington, found it very fast compared to taking the tube all the way from Heathrow.

It isn't cheap though (£16.50 one way) for the 15 minutes to are on it!

Instead of the Heathrow Express which takes 15 minutes to get to Paddington and costs costs £18 when you buy your ticket at the airport (or £23 if you buy it on the train), catch the Heathrow Connect. It takes 27 minutes but only costs £8.50 one way. It still brings you into Paddington Station and is a very good alternative.