Varies from 2-10mins depend on time of day. I tend to log on, do a random BG to warm up then jump into arena queue. My first game is normally up quickly and from there I tend to head out to Deepholm or TH (wherever my questing is up to) and just sit in the queue as I quest. I can normally get through 10 games in a night in under 2 hours and do this on average 5 nights a week.

This is on Bloodlust but I play on Western Australian times so well off kilter with peak US times.