Neither the ballistics skill nor the heavy weapon skill provide boosts to the damage output of the Bridger grenade launcher. Both include the Bridger in their perk art so I believe we can assume its an oversight.
The Bridger has two sources of damage, first the projectile itself does some amount of bulk damage and then the explosive does splash damage of a lesser amount. Currently the only perk effecting it is explosives and it effects both, ideally I think the explosive splash would be effected by explosive and the main damage would be effected by heavy weapons and ballistics
1.8.86.0
Yes
Spawn the bridger weapon or any variant, test damage or verify using in game menu, apply ballistics or heavy weapons perks and test again