Wizz Air fly from Luton to Bucharest:
http://wizzair.com/?language=EN
They normally use Baneasa airport but between 10/05 and 31/07 Baneasa is closed and flights are transferred to Otopeni airport. For some random dates I've just tried in June, single flights were all priced between �39.99 and �59.99
Wizz Air's flights are probably the cheapest you'll find but you might want to check the fares with Romania's national carrier, Tarom:
http://www.tarom.ro/en/
(They fly from Heathrow to several airports in Romania)
Chris