You are encouraged not to walk across the downs alone late at night, but I haven't heard of anyone being raped or mugged there. It is very well lit and a massively student area so you should be fine. The issue with the downs is that it is a popular dogging spot, but as long as you don't flash your lights back at cars, you won't notice it.
Contrary to what History Lost in Physics says, I believe the Gloucester Road/ Stokes Croft area is actually pretty safe. It's seen as a poor and therefore down-and-out area but is actually a friendly and thriving community. The only real issues are fights between local gangs.
As a girl in Bristol I feel FAR more unsafe walking along Whiteladies Road after 8pm on friday and saturday nights. Its full of lairy ***** looking for fights and their whiny girlfriends wearing next to nothing. But again, they probably won't harrass you as they're too busy arguing amongst themselves. There were lots of sexual assaults around the Whiteladies/ Cotham Hill area last year, but supposedly it was one man and he was jailed.