Diemmess: you ask 'what have you done?' The answer is - not read the installation instructions properly... :-) It is unfortunately true these days that, if you accept all the defaults without checking what those are, you'll end up with stuff you didn't want. The Ask search bar is a particular culprit. Next time, take it a bit slower...
In Chrome, if you go to 'settings' (the menu you get when you click on the three horizontal bars top right) you'll find an option to choose your search engine. Just change that.
As for removing the Ask bar - you may well find it in add/remove programs.
As you predicted not quite as easy as it looks. I managed to make the taskbar option disappear, then moved to Control Panel add/remove and got rid of ASK and its update. Threw in in a session with CClean and a re-boot as well.
If I put a word to the Search window it now seems to depend what I have done with this site before if I had used Ask, Ask is still the response but if it is something really new then Hooray I'm back to the Google.
Have more urgent things to do now, but unless I can fix this, I will go back to a recent Acronis backup.