We have to catch a flight out of Stansted back to the US. Our intra-Europe flight at LHR Terminal 1 has been moved so that it now gives us only 50 minutes from landing to National Express bus departure for Stansted in order to make it to Stansted 2 hrs before our flight home.

We have to go thru immigration and may have to get luggage (trying to do only carry-on). For those who have made this trip, realistically, can we make the bus? Or should we just contract with a private car company for the trip?
I already know we can't take the train due to weekend delays/track work.

Thanks for any help!