I'll volunteer a concrete answer... this is not something I would EVER try.
BG botting is considered very high risk botting behavior. PvPers are serious about their game, and will report even real players if you're not "playing your class right".
Also, keep in mind we are expecting a large WoWclient patch next Tuesday. This will cause all kinds of problems for a Relogger if it is running.
If you do actually decide to take this enormous risk, install TeamViewer or LogMeIn so you can access your computer from another computer and/or phone since it's likely to encounter problems not to mention the new content patch which will probably put your bot on hold for a couple of days. To answer your question, it only takes 1 bg for a player to report you for doing something they don't like.