I've played the game with bots now for a few hours, and here's what I've observed:

Works:

• Auction bots - Wow!  Lots of great and useful stuff in the auction house, plus they bid and buy your auctions.
  
• .bot add character - Reliably logs the specified character from your account into the game as a bot
  
• .bot remove character - Reliably logs out the specified character from your account
  
• inviting any bot to your group - Always works if it's one of yours, and random bot either agrees or declines depending on level difference
  
• Default behaviour of bot in your group is to protect you / assist you (depending on class) in a fight, and collect crafting materials when available for their professions (skinning/mining/herbalist)
  
• /whisper character - Once whispering, you default to whispering so don't have to retype all that every time and just enter the desired instruction to the bot
  
• /whisper character help - Gives "help" information of available commands.  Kind of confusing actually.
  
• /whisper character follow - If you're within sight, the character will follow you, including mounting if you're mounted, or using a flight path.
  
• /whisper character stay - Tells the bot to stay put
  
• /whisper character grind - Bot will begin to attack every enemy in sight to gain XP, but will try to stay within a certain range of you.  I couldn't seem to get my bot out of this mode without logging it out and back in.  Certainly does clear out an area (if you have a high level bot) in a hurry.
  
• /whisper character r shift-click reward name - shift-clicking the name of a reward in the bot chat output is supposed to insert that item into your chat input.  This is how you can tell your bot to pick a specific reward to complete a quest.
  
• /whisper character accept shift-click quest name - shift-clicking the name of a quest in the bot chat output is supposed to insert that quest into your chat input.
  
• /whisper character revive - when near a spirit healer, revive the dead bot (from their ghost)
  
• /whisper character release - release bot's spirit when dead (makes them a ghost)
  
• /whisper character trainer learn - learn everything the bot can from the selected trainer
  
• /whisper character repair - If talking to someone who can repair armour, instruct the bot to repair theirs.
  

Works, sorta

• /whisper character accept quest - Sometimes bots seem to default to accepting quests, sometimes they need to be told explicitly to accept a quest
  
• /whisper character accept * - If using the quest name doesn't work, sometimes using * will
  
• /whisper character accept all quests - Supposed to change the default behaviour of the bot, but again, not reliably
  

Problems

• Bots fall through the earth, or get trapped in trees sometimes.  If you can't free them just by moving around (and having them follow), and it's one of your characters, try .bot remove and .bot add.  Sometimes they come back freed.  If that doesn't work, you'll have to .bot remove, logout, and log in as the character that was a bot.
  
• Feedback from the bot, especially when trying out commands..  either it gives you the default help message, or stone face silence.  Neither of which actually helps you figure out how to fix your command.
  
• Combat - Usually the bot is super helpful, and fights better than I could ever hope to do.  Sometimes though, it just watches like a bastard.  Try moving around.. maybe the bot is in a poor position to do anything.
  
• Aggro - Just like pets/minions, bots move around you, so can aggro nearby mobs you're trying to avoid.  Be prepared.
  
• Movement speed - This isn't the bots fault, but if you're a faster runner, and out-pace your bot, eventually it will complain "Wait for me!" and if you get completely out of range it will just stop following.
  

Untested - I'll move it to the appropriate section once I try it.

• /whisper character summon - if you're in an inn, supposed to bring the bot to your location.  This would save a lot of travel time, and effort getting bots unstuck.  When I tried it, the bot whispered back that I could not summon them.  So I guess there's some requirement for summoning I need?
  

FYI - I was unable to log out of the game this evening... I played for a quick 30-45 minutes at the end of the work day and when I went to log off/signout it told me I couldn't because I was in combat.  Actually, I was in a small community with friendly NPCs that bought, sold and gave quests.  I was finishing up because I had just solved a quest.  I'm guessing that it might be related to a couple mobs that I aggro'd on my run back to the quest giver, but I had been there for 5 minutes selling my gear and completing the quest while starting a new one and the mobs were nowhere to be seen.  The only way I could get out was to alt-ctrl-del and shutdown WoW from the Task Manager.

That's not at all bot related.. that's just the server being the server.  I've had that before, but not for a long time.  I suspect I had to do the same as you did.