I honestly don't think this would be possible given the current restrictions of the mIRC scripting language.
If you want to host an IRC bot, and you have a DSL (or better) connection, then it's easy enough for you to host it yourself, rather than have to hassle with a website. I myself host 4 IRC bots, and while things can lag a bit when the system is busy, that's mainly due to the fact that the other computer I have on my network is down at the moment, so I've only got one system running lots of things.
To host your own IRC bot, you'll need an additional installation of mIRC (to act as the bot), scripts (either downloaded or written yourself), and a decent internet connection. I don't recommend anyone try to run an IRC bot if they're using a dial-up connection.
If you have more detailed questions, give me a shout & I'll be happy to relay my own experiences with hosting a bot.