Lions lacked tempo, fluidity and above all conviction but managed to do just enough in front of goal to book a place in the second round.
Bolle helped himself to two goals, with Bern and Ricky Engleman chipping in to complete a 4-2 victory.
Lions boss Tony Gold said: "A win is a win and that is what Lions will take from what overall was a poor team performance."
Lions: Mario Cenolli (sub: Dan Lee), Ricky Engleman (sub: Tony Gold), Danny Berg, Michael Sacks, Adam Myeroff, David Soutar, Aron Barnes (sub: Andy Glynne), Ben Ellis, TJ Keterman, Daran Bern, Adam Bolle
Scorers: Adam Bolle (2), Daran Bern, Ricky Engleman
Man-of-the-match: Michael Sacks