Quite a few birth control options for women tend to play havoc with sex drive. I know a friend indicated they went from wanting to have sex multiple times a day when not on the pill to only a few times a week when they were on it.

My girlfriend doesn't get as lubricated now that she's on the pill as she did when she was off of it. She hadn't had sex/masturbated prior to us dating, so not sure if it's had any impact on her sex drive.

Not the depo shot specifically; however, the majority of the hormone based birth control has similar side effects regardless of the kind. But if that's a concern, you may want to look into a non-hormonal option. There are non-hormonal IUDs if memory serves.