Where to park in Bristol for the Bristol- Bath cyclepath?

A couple of options assuming you are arriving into Bristol from the M32 - you could park in the Cabot Circus car park at the bottom of the M32 - the start of the cycle path is 5 minutes away. Alternatively, you could come off the M32 at Junction 2 and follow the signs to Fishponds and on Fishponds Road park on roads such as Elmgrove Road or Brenty Road, cross over by the Morrisons and the cycle path runs across the top of their car park (I think their car park has a time limit).

Assuming you want to do the whole thing, you can park very close to start of the path. 

The best option is on-street parking which you pay for on a meter or with the ringgo app. Park anywhere near Bakehouse cafe (which is mediocre by Bristol standards but a useful marker). St Phillips rd or any of the roads around there. Check the meter as there may be a 3 or 4 hour limit though, which may not be enough depending if you are planning to spend any time in Bath.

Failing that, a short distance away there is Gardiner Haskins car park. You will see blue cycle route signs straight away. I'd say that would be a better option than Cabot Circus car park which is a massive multistorey and further away. 

If you don't mind missing the first section of the path, then as said above, aim for Morrisons in Fishponds. Or alternatively in Easton somewhere (you can see on Google maps there are lots of entry points). That would likely not cost anything, but it's a bit of a maze if you're unfamiliar with Bristol.

Note that the first section of the path has a bad rep for muggings etc, mainly at night/early mornings. During the day it's sufficiently busy with other cyclists I wouldn't worry too much, but worth mentioning.

Peterfrommearth has it spot on.  Gardiner Haskins car park for easy, all day parking (at a cost) and it's a straight shot to the cycle path.