Today when I was browsing all of a sudden my cpu/memory usage went up and task manager showed a process setup.exe with description "Google Chrome".

Is google trying to install a virus because my homepage is set to bing?

Or is setup.exe the installer for a new version of chrome from the auto updater?

I just want to make sure because I don't like random setup.exe processes starting up without some kind of notification, however subtle.

The last update I downloaded manually was named chrome_installer.exe, I didnt download the last one manually so it might have changed.
Also Im using the Dev version, so other versions may differ.
Next time, check what directory this setup is being run from, that may shed some light on the issue.
You can use Sysinternal's (awesome) Process Explorer to find the directory (among other things) of the process and also suspend it while you check it out.....
http://technet.microsoft.com/en-us/s...rnals/bb896653

I just want to make sure because I don't like random setup.exe processes starting up without some kind of notification, however subtle.

Totally agree, Im not much of a fan of these silent installs either.

Is google trying to install a virus because my homepage is set to bing?

No. Some of Googles practises might be a little bleh, but their not that bad