I will be on vacation in London at the end of this month. I arrive to
Heathrow airport and stay in Bayswater inn hotel. Let's just say that $100
price for the taxi trip seems to be somewhat excessive for this New York
resident . So I figured I can take a tube.
http://journeyplanner.tfl.gov.uk suggested this route (I selected tube only
with least transfers):
=======================
10:00

10:06Heathrow Terminal 2
Walk to Heathrow Terminals 1-2-3
Transfer time:6mins


10:06

10:39Heathrow Terminals 1-2-3 Underground Station
Take the Piccadilly Line towards Arnos Grove
or Piccadilly Line towards Cockfosters

10:45

Earl's Court Underground Station
Take the District Line towards Edgware Road (Circle Line)

Average journey time: 8 mins

10:53Bayswater Underground Station
=======================================

Is this route doable with one large bag on wheels and small backpack? I've
never been to London and don't know how crowded London Tube is. Am I correct
to understand that tube trains run on pre-determined schedule (seems like a
foreign concep to me )?

TIA