is there an easy way to upgrade the bot or do I have to start over from scratch again?

Differences between 2.10 and 2.11 are small and you can easily upgrade by hand - even if you use lots of custom modules.
The main change is AOChat.php, which no longer needs aokex. If you want the bot to display the new version number (and probably if you are running bebot on windows), you may want to use the new main.php as well. The new php.ini makes the bot log a bit more php problems, the new start.php is smarter, but not really needed to run the bot. In the modules directory, it is the files Calc.php and Items.php - but most people already use the new version of Items, and will rarely encounter the calc bug.
At least when upgrading from 2.10, I see no reason to drop the members table. But it's not like it hurts to do that.

If you run older versions of the bot, then... no idea. If you can read php and know how to use diff, it is not hard to find the differences between 2.11 and your old base bot. If that is worth the trouble is another question.