I've never been 3 hour temp banned when just running AV (which BTW isn't even a real ban, had this ban probably 4+times in the last 3 years... Only once with HB and other 3 with just macro clickers) But as soon as i started running random BGs to cap conquest on my alts weekly i received it. I think more so of then getting reported AFK the bot sometimes screws up and will AFK it self out, which this then counts towards this 3 hour temp ban (or longer depending on how long its been since you were 3 hour temp banned prior, think after your 5th ban its 72 hours or something? then perm on the 6th)
Outside of events such as Christmas/Halloween I've never been called out, whispered, or afk reported in AV. During the Christmas/Halloween due to the stupid tree's/punkins I've had people whisper me asking me why I'm humping said object, maybe 1 or 2 afk reports out.
BG botting isn't safe at all, but I've botted 5 characters now, 5 fully BG geared and 4 upgraded and only once have i been 3 hour temp banned with HB. Just don't run random BG and you should be safe.
Safe BG's I've found so far in order of which are the safest... AV - EoTs - AB - Stand - Everything else especially any of the flag BG's are risky.