Pont du Gard

Looks like the bus is still the A15 I took from Avignon to Pont du Gard in 2017:

https://www.edgard-transport.fr/horaires_ligne/index.asp?rub_code=6&lign_id=6&sens=2&laDate=01%2F08%2F2019&heure=5&minute=15#dateSelection

You don't have to book the train ticket to Avignon in advance (make sure you take the train to Gare d'Avignon Centre NOT to the Avignon TGV station which is a ways out of town!). I actually day tripped from Arles to Avignon and from there to Pont du Gard by this bus. I didn't have luggage to store; maybe you can stow it at the train station there or the adjacent bus station. But note there aren't a lot of buses during the day.

I did this is June and took the 8:45.
According to Rome 2 Rio these are the times: 6:40 AM, 8:45 AM, 11:40 AM which matches up with what I remember.
The line is A15: https://www.edgard-transport.fr/horaires/?rub_code=23

The bus station is underground below the Ibis hotel just the right of the train station as you walk out. There is no left luggage/consignee at the train station but there is a place in town about 5 minutes walk from the train station.
https://pro.provenceguide.co.uk/533/new-la-consigne-luggage-lockers-in-avignon/

The town is right across from the train station - cross the street and enter the ancient city gate and you're there. The left luggage place is a few minutes down the road. Or you can try your hotel but keep in mind you will need to cross from the train station into town, back to the train station effectively to get to the bus so allow enough time.

The bus driver is used to everyone getting off at Pont du Gard so don't worry that he won't announce it or anything. The return bus stop is across the roundabout by the wall just a little down the road. Check the return times and plan accordingly.
1:20 PM, 3:15 PM, 5:30 PM, 6:45 PM

I did the 8:45 to 1:20 and it was certainly enough time.

Enjoy,
=Tod

Check the schedule; in the summer, I think the bus will drop you in the parking lot of the visitor's center. In May when I visited, the bus dropped you at the edge of a traffic circle about 1/3 of a mile from the visitor's center. (Not really a big problem, as long as you are aware.) A Friday in August may not have the same schedule as a Friday in October.

Don't worry it is a popular tourist site so there is no problem getting there and back; you will see the tourists speaking different languages going the same way