We'll see what others here say about my suggestion...
I would think about picking up your permit the afternoon of the day
before your trip begins.(No later than 4:30PM)
You should be able to do that at either the Polebridge Station or the Apgar BC Office.
Verify the pickup hours at the Polebridge Ranger Station.
I suggest that early permit pickup because backpackers share the same parking lot as day hikers.(There's signage for that lot)
However,
you want to be through the Polebridge Ranger Station gate
long before the 8AM office opening...imo.
You want to beat the day hikers to the parking area. Having permit in hand you can drive to Bowman Lake as early as you like.
And going early(anywhere) is a good idea given the crowds in recent years. It just ensures fewer hassles.
Nicer hiking early too
pete