To access internet in college, we need to authenticate the IP and MAC address of our machine at a certain college portal. Earlier we used to have to provide proxy authentication every time the browser opened, but they changed it to this recently. However, technically I am still accessing the web using my college proxy(right?). Does the proxy track and log my Tor browser bundle history?
No. Unnless they have direct access to your machine(malware / trojans) they cannot see your history.
Unless they are running endpoint (client) tracking software, it's unlikely they will be able to see your Tor browsing history.
However, they can see the dates/times when you're using Tor, as well the dates/times that their own web services were accessed via Tor. They might be able to do some traffic correlation.
They cannot see your history in the sense that they cannot see what you are doing on Tor. However, unless you're using a bridge, they can tell when you're connected to the Tor network. Below is the most memorable example of someone misunderstanding that concept:
 And even if you were using a bridge, they could find out if they were trying hard enough.
If in some period of time Firefox (on which is based TBB) or any other browser you are using is vulnerable to 0-day exploit that allows on remote attacker to access parts of the browser memory or files - yes, only in this case, someone can read your history / bookmarks / settings, etc. But serious vulnerabilities like this are rare in browsers, so just be sure that your software is up-to-date.