I'm sorry if I am being ignorant here, but having just got off the Bristol website myself, i get the impression they want a little more than GCSE's A-C. If there truly are only 5 places, (which i haven't come across that and i hope its not true as i hope to apply sometime next year) surely it would be more competitive than 5 GCSE's A-C, surely if anything it would be more like AAAAA possibly AAABB. Below is what I copied from the website.
* BTEC National Diploma in an animal or science based subject (3 Distinction grades)
* Access to Science or Medicine (70%, Distinction, or 60 credits with 45 at level 3)
* City and Guilds Advanced National Certificate in Animal Care (to include the Advanced Science option)
* Mature students returning to education from the work place will also be considered.
To the best of my knowledge, a BTEC can be the equivalent to GCSE's or A-levels depending on the level of study, they mean DDD by distinction grades which is the top. An access course with 70% distinction is extremely good and of course people will have higher than this. Also consider that these access courses are specialised in science or medicine at a higher level than GCSE(A-level upwards), so will look better upon application. City and Guilds Advanced National Diploma is similar to A-levels and with it being specialised in Animal care it means applicants will have an upper hand than yourself who just has general GCSE's.
I would consider doing your A-levels now and entering after completion of them, if i had a chance to re-do my A-levels i would make sure to do Biology, Chemistry, Maths or Physics, some universities like English too so perhaps that as your fourth for AS, then if subjects get too hard(which unfotunately they do) drop it at A-level so you just have it as an AS.
Best of luck with it all, I'm in the same boat only alot older, well...20 which means all my academic mistakes are catching up with me now i want to become a Vet. So i hope i can help you to not make similar mistakes!
*Crazy Izzy...if offered you should definitely take triple science(high SAT's required), i was offered went to one class was too lazy back then and too interested in hanging out with my friends...big mistake! It is a great opportunity though hard going, but will set you up for when you (presumably) do your A-levels. Language is always a good one to take too as you open up your options with places you can live and it looks good on your CV etc. So French or German i presume unless school has changed so much from when I was there! Just concentrate on getting good grades in the sciences and maths, 3/4 A's (depending on if you are taking double/triple science) in these areas will reflect higher than consistent B's in all subjects(of course don't fail your others). Try to get an A or B in English Language and Literature too as of course these traditional subjects are viewed highly.
Best wishes,
Louise Roberts