It's officially possible to have the bots go in the jungle
The bots in the up and coming MOBA Paragon regularly go into the jungle, and not just following a player their attacking.
The bots in Paragon go into the jungle on their own to capture objectives (in the form of harvesters) AND they even use wards. I have been walking in the Paragon jungle to randomly encounter bots that were doing their own thing in there, and I've had bots come in to get me when I was near an entrance/objective (bot not visible from lane), implying that they had a ward there so they knew I was there to be attacked.
It's actually kind of funny when I play too many bot matches in LoL then play one in Paragon, because I'll actually forget bots go in jungle and they'll catch and kill me when I'm at low health from fighting jungle camps.
Not only has Paragon proven it's possible to have bots use the jungle, but given the differences between the games I have to imagine Paragon is harder to code than LoL.
Time to get your bots jungling Riot.
For anyone who might say to me "then go play Paragon": I do. I play both games. LoL is isometric whereas Paragon is third-person, which alone makes them very different games, so I play them both at different times based on what I want.