If you leave the bot on 24/7 the time to 85 will be infinite. I'm estimating about 2.5 days played before you're banned.
I have not been active on the forums, but after I seen this post I had to comment.
Please don't listen to this, stupid post, I'm sorry but it's true. If this was the case I would have been banned many times.
Don't go round spreading roomers that are UNTRUE.
Now @ OP:
If using heirlooms you can hit 85 in about 5 or 6 days /played. As others have said depends on the class, but say a Pally or Druid, Priest could hit 5 days /played.
Also 24/7 will cause bans to happen more often. But it all depends on reports, I believe. I mean there are people who can and will play many days in a row without a break, such as people highly addicted to the game and people with conic illnesses ect and I'm sure there would be many others to. If blizzard see a account logged in for 48 hours with out a break and they get reported for botting well they would take a much more detailed look into that account compard to somebody account who has been logged in 30mins and sombody reports them for botting ect.
My advice bot for 12-14 hours per day and it will take around 4 weeks to get to level 85 and level your proffs to max and make around 10k gold.
All of this is my opinion, I have no idea how blizzard works. But using common sense and doing a fair bit of research on bans this is what I have come up with and my "main" has NEVER been banned.
EDIT: Use Kickazz profiles, those are the best for alliance leveling that I have found, as for horde I am not sure. But if your going to use HB I would highly suggest rolling Ally as the profiles are much better then horde!