Can I request Apple to expedite the approval of a new version of my app to rectify a critical bug If my app is live and users are facing a critical issue, can I upload another build and ask Apple to make it live within a day or two?
Yes; there's a feature called Expedited app review precisely for these cases. From my personal experience, it takes usually about 24 hours to complete, but that's no guarantee.

From the linked page:


  Expedited App Review
  
  If you face extenuating circumstances, you can request the review of your app to be expedited. These circumstances include fixing a critical bug in your app on the App Store or releasing your app to coincide with an event you are directly associated with.
  
  Urgent Bug Fix
  
  If you've submitted an update to fix a critical bug in your app on the App Store and you are requesting an expedited review, be sure to include the steps to reproduce the bug on the current version of your app.
  
  Time-Sensitive Event
  
  For apps associated with an event, we recommend you plan and schedule the release of your app in iTunes Connect. However, if your app is still in review and the launch of your event is quickly approaching, you can request to have your app review expedited. When submitting your request, it's important to include the event, date of the event, and your app's association with the event.
  
  Please Note: Expedited reviews are granted on a limited basis and we cannot guarantee that every request will be expedited.


It's a (partly) automated process, you can just sign in and request one on the Developer Portal.