Have you even flown before?
You check in from Manchester. You get both boarding passes. Including the one for Bucharest which will have the boarding gate already . At AMS, you check to see which gate you're supposed to go to and you go to that respective gate. You DO NOT HAVE TO GO THROUGH IMMIGRATION / CUSTOMS as you're transferring from international to international flights.
55 mins is fine for AMS.
Welcome to Flyertalk , anyway. Do come back and tell us how it went...