Pulse Width Modulation ... even I know that! EDIT ... Tony beat me to it!
Had a thought this morning ... as this is a lash up printer, what's the need to drive the heated bed from RAMP and Marlin?
It only has to be switched on at the start of a print and off part way through or at the end. So why not use a little Willhi or similar on, off temperature controller in combination with Kinghtys great suggestion of a car relay.
A quick and simple fix ... about £6 quid from china and about £12 - 13 from the UK ... or I've got a brand new 220v one you can borrow.