A 'botgroup' is a normal group comprised only of bots.
There is no way to include a client (or merc) in a botgroup..however, you can have other people invite your bots.
You should be getting buffed when you invite a bot into your group.
The spell ai code doesn't discriminate against clients
If you're not getting buffed, the first thing I would check is if they have enough mana for the spell they're trying to cast.
Next, look at blocked spells.