I'd be untroubled by the 1:15 connection time in most of Europe's major airports.

My only suggestions, based on experience, though not in Bucharest, is to be early for your flight departing the US, and carefully matching that, when it comes departing Bucharest.

Not knowing your European connection city, I can't comment how much time security and "pre-clearance (US bound flights) may be required. Prague and Madrid seemed slow, but "pre-clearance" in Dublin was a breeze. In either direction, terminal changes and the ever-present crowds at LHR can slow you down.

Others here may provide better and more detailed info.