If you are trying to do this hobbyist style your best option is likely the Raspberry Pi (Not an Arduino). Its a full microcomputer that can run Linux. It has USB ports that could host a USB camera (provided you can find drivers) and it has ways to send video out. As mentioned you won't get video over Bluetooth, but you could send it over WiFi. There are other options, but this is by far the one with the best community support.
If you just want wireless video you might look into FPV gear sold by HobbyKing or similar sites. They have a lot of reasonably priced 2.4 and 5.4 GHz transmitters and receivers that let you send and receive video in real time. I didn't see any that supported USB cameras, but that doesn't mean there aren't any out there.