Say I made a bot and then I didnt want it on this one website anymore. The bot isnt protected by copyright laws or anything, but do I, the owner, have any rights in this?

You have an informal copyright hold over the software if you can prove you created it.

Which is easy if you alone have the source, and your name is on it.  You should be able to find a cease & desist template somewhere online which you can use.

And if they fail to stop?

Do a whois lookup on the domain and contact their host.

[quote author=rabbit link=topic=15216.msg154774#msg154774 date=1151002863]
Do a whois lookup on the domain and contact their host.
[/quote]
...followed by a handy dandy DMCA letter.