Is it possible to unlock more champions for bots in LoL custom games?
Solution 1:
No, at the moment you can only use the ones you mentioned. The only thing you can do is choose wisely between them. RIOT really tries to encourage people to play against other people and not vs AI.
Solution 2:
Now, you can choose more characters then those. But only a few more, such as Wukong, Garen, Caitlyn, Ziliean, and others. Not all of them are availiable though. As the previous answer said, Riot encourages you to play with others. But, yay! More characters!