I live in Bristol, so me and a few mates will walk down. Assuming you're driving from Cov 2 hours sounds about right, maybe a little less if the traffic is good.
As for parking, Bristol is generally pretty horrendous. Definitely not a city built with the car in mind. The Ashton Gate area isn't as bad though, there are a few car parks around that will offer matchday parking I would imagine. Probably best to get here a bit earlier though.
I am coming from Devon, the best place to park for the Ground is at Bedminster Cricket Club (BS3 2JX), Ashton Gate isn't even five minutes from there, will set you back £5.
Where is everyone drinking? I will be there all day in meetings and will be going on my lonesome! work paying result! and to answer the OP just under a 2 hour drive door to door.