Most bots are just another IRC client, that you host on your own PC. So with those, you would still have to keep your computer on at night.
The alternative is a Eggdrop bot.
These are written in TCL I think.
You can host these bots on "shell accounts". But these shell accounts are only running with Unix/Lunix and you have to pay for these.
As far as I know, there is no easy solution. Other then creating an eggdrop bot (which is not easy), and creating a shell account (which costs money and is also not easy).