Hey
I know it must seem very frustrating to you about RVC but I think even if you appealed it would be highly unlikely for them to reconsider. They do make it very clear in the requirements that you need 4 weeks within 18 months before applying. I think they would need an incredibly good reason for you not having it and unfortunately I don't think yours would cut it.
Here in the UK it is also very difficult to find placements before the age of 16, mostly due to insurance reasons, so everyone is in the same boat there.
Unfortunately there is high competition and you are competing against people who have managed to get well over the requirements - all starting after the age of 16. Sorry I can't be more positive.
As for postgrad - I don't know the exact statistics but I would say that entry is equally competitive. I know this year RVC have 98 places on the PG course (which is significantly higher than previous years but they have now reached a limit and that is the maximum they can take).
The only unis that currently do a shorter 4 year PG course are RVC, Edinburgh and Dublin (but they have very few spaces). However, with a degree you can apply to any of the 5 year courses as well. Statistically if you apply for 4 year at RVC they will also consider you for their 5 year course so you could say that helps your chances if they consider you twice and it only takes up one option on UCAS.
I would have thought that animal science at bristol would then be eligible to apply for 4 year vet med (no guarantee you would get in with either biovet or animal science!) But before accepting a place for animal science I would contact all of the vet schools to double check that it is acceptable.
I have personally loved my time at RVC doing biovet but I can't really comment on Bristol as I have never been there and don't know much about the course so its hard to say which is 'best'. I think that comes down to what you want to get out of being at uni so how you would personally define best!
If I were you and you are really serious about becoming a vet, if you don't get a place this year, work hard this year. Get the best grades you can possibly get. Spend the summer getting work experience requirements sorted out and apply again this year to start in 2018. Take a gap year, travel, do work experience, earn some money whatever works for you.
This is definitely the cheapest and fastest option for you. If work experience is your only issue and academics are good - take a gap year and get the experience. There is no point spending 3 years paying £9250 a year on a degree you don't want to do when it is well within your grasp to get a place.
Hope this has helped