Terror
It really depends to which part of the M4 or M5 you are heading. If going to/coming from Devon, Cornwall or most of Somerset you would be advised to use the A 38 to the south, ie away from the city of Bristol, and join/leave the M 5 at East Brent, north of Highbridge/Burnham-on-Sea.
If travelling to/from the east on M 4 (ie to/from London direction) you may well decide to use part of the central area around Temple Meads and Old Market to access the M 32 and then M 4.
If travelling to/from Wales on the M 4 or to/from the Midlands on the M5 the best bet would probably be via the Bristol City Football Ground, Cumberland Basin, the A 4 Portway (under Clifton Suspension Bridge but Clifton is the suburb above you on the hill, you are not driving through it) and Avonmouth.
There are plans to build a link road between the A 370 and A 38 which would remove part of the sometimes admittedly tiresome trek through the south west suburbs around the City football ground.
It is a great shame that the City forefathers were not blessed with greater vision because they could have had Filton as their airport in the 1950s. It's too late now. It was tried in the mid 1990s and went to a Public Enquiry but the NIMBYs won the day.
So Bristol has to make do with what it's got and, in fairness, despite many physical disadvantages as to location, access, size of site, weather and limited runway it hasn't done badly.
This thread has strayed a bit from its original theme but I suppose ease of access is one of the things that a potential carrier would take into account, although I am sure that the number of potential pax would be the number one criterion and the aforementioned disadvantages don't seem to have put off pax from using BRS on other routes.