You will have plenty of time if you go straight to the DME bus.
The drive from OIA to Pop is about 30 minutes,so even with a long wait to board the DME bus,you will be fine.
Also,if the Gondolas are not running,DHS is only a 5 minute bus ride from POP and you can walk if short on time or boat easily from DHS to BC.
Walk from Plane to DME----15 minutes
Wait to board DME and leave OIA----0 to 30 minutes
Travel time to POP----30 minutes
Wait for POP bus to DHS----0 to 20 minutes
Travel time to DHS----5 minutes
Walking time to BC----20 minutes
Total time----70 minutes to 120 minutes
So the worst-case 120 minute time would put you at BC at 4:50 leaving another 70 minutes for WORST worst-case!lol