I would say 45 minutes? But return seemed a little faster.
If you do go, when you get off the bus at PP, walk right (facing the water) all the way to the end point where there a restaurant. That is where we camped. Decent rest room inside, picnic benches, outside bar, inside tables.
Lounge chair situation was a bit different......where the bus drops you , a little bit to the right was an ice cream stand where you collect a ticket for $5 per chair. Then you go to the lounge chair guy and stand in line and get him to put your chair where you want. We paid him $10 tip to bring our chairs to the restaurant area all the way to the right hand corner. One can also drag their own lounger. No umbrella was required where we were....lots of shade. This lounge chair business was what many people had complaints about, but we managed it. I do agree that Celebrity could have managed this better by pre reserving chairs or spaces/areas for their excursions, but we were the first cruise to Tobago, so may be now it is better managed. Pigeon Point is their national park, so it is open to all and that day there were many people, but on on each others' backs.
The port area had very few vendors set up (five maybe?). I got a christmas ornament from a local artist which I have posted picture of here as well. Port looks big but not a lot there if you just stay within. Once you dock do a visual survey from the ship to check it out.