Huwag mong bulagain ang bata.
Don't startle the child.
The 'Eat' part is English and it has something to do with the fact that the show comes on at noon when people are about to have lunch. When it started in 1979, the show's title was written as Eat... Bulaga!
You're starting to eat lunch and then the comedians come on the television to surprise you. Eat... Bulaga!