I recently leveled a mage 79-90 by pet battles in the forest part where dalaran is (you know I bot when I don't know the names of places on the map). I got to 90 in a about three days just doing pet battles with three beasts. I'm not sure I would recommend it though cuz I just read online about the unborn val'kyr and from what I understood people camp it pretty hard core to get one. Yes I did get one.
The same mage I used kicks profiles, but with questing comes a little baby sitting, HB might get stuck at a flight path, or maybe a quest giver could be incorrect... etc.. It has happened to me plenty of times to understand that if you pack up and leave town for a few days will I be at level 60? Probably not without baby sitting, but if you do need to check I use logmein free and use to remotely monitor sometimes.
You never know with doing dungeons.
other ways to xp involve gathering, so ores and herbs, also with archaeology. I used to basically level 60-70 using archaeology. It wasn't too bad, and there was a plugin to basically kill yourself if you got stuck.. This was nice because it almost guaranteed not getting stuck in the trees forever. So a suggestion might be to do petbattles, herbing and mining and archaeology at the same time while you can fly in eastern kingdom etc.. Oh wait you wont get much xp herbing mining in eastern kingdom..
As far as 1-60 goes, the only sure way is basically grinding, but I would never do that or suggest doing that. But with a relogger and a grinding profile it would be the most guaranteed to stay online without any snatches. The profiles have to be good as well. Maybe if you have a higher level toon you can fly to areas using the plugin that creates profiles for you and just create paths for yourself so you aren't using a spot that may be more commonly used... or you can use the commonly used ones, but that is up to you.
I guess what you can really get out of this wall of text is that bots that require more logic etc tend to get stuck more frequent. Easy repetitive things such as grinding would be more guaranteed, but in my opinion would be more dangerous. Thats why I usually wait until I can fly to do archaeology etc.