Rhys Priestland, Wales' current first choice fly-half, is part of the 16-strong party heading to Australia earlier, leaving Biggar the chance to stake his claim for one of the 18 remaining spots on the tour.
And Biggar is determined to make sure he has a place on the plane.
"Rhys has done superbly well over the last 12 months," said Biggar.
"He quite rightly deserves to be number one in the squad at the moment.
"We know where we are in the pecking order and it is about trying to change that pecking order.
"There is no point me being happy to be on the bench, or having a holiday, because I want to be pushing all the way.
"I am just really glad to be back and really looking forward to Saturday and, hopefully, if I get on the tour, pushing for a place out there.
"We are aware that the first-choice team flies out [early] and it's up to us, stepping up to the plate and showing we are competitive.
"There are a lot of guys pushing the starters all the way and a good game against the Barbarians will do our cause no harm."
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