I ride parts of it most days.
Which bit are you thinking of? Or are you considering the whole route from Oxford into the smoke? I've done it on a bike from Reading to Windsor and from Maidenhead to Kingston, without a problem. It's a bit dodgy through Staines (but what isn't

) but I had not problems riding it.
Oh, hold on, you said "Thames Path". I'd look at the
Sustrans Thames Valley Cycle Route, they do a fairly good route map and (the clue is in the name) it's designed for bikes rather than walkers.
And, if you want to come and have a play, let me know and I'll recommend some good cake stops.
