The Florida-based Pegula made a business-like job of wrapping up the first set before Bucsa, 25, had really settled.
Pegula then raced to a 4-0 lead in the second, getting the better of the baseline rallies with pounding groundstrokes.
But Bucsa found some form mid-set, producing deft drop shots and fine angles to claw back four games as Pegula's intensity waned.
"I definitely feel I can go deep here ... a short-term goal to get into the second week."
Pegula will meet Italy's Elisabetta Cocciaretto in the third round.
Persons:
Jessica Pegula, Spain's Cristina Bucsa, Dylan Martinez, Cristina Bucsa, Pegula, Bucsa, Italy's Elisabetta Cocciaretto, Clare Lovell, Ken Ferris
Organizations:
Lawn Tennis, Croquet Club, Spain's Cristina Bucsa REUTERS, Dylan Martinez LONDON, Wimbledon, Thomson
Locations:
London, Britain, American, Florida, Pegula