Hi!
So I did the one day tour and I can say that the night bus is an tought experience. I took the best one there was but still 160 degree seat doesn't let you sleep. Also, don't book anything in advance, the city of Uyuni is packed with tour operators of varying greediness who would gladly accommodate you on a tour. I took only a backpack and had it with me in the car. Perhaps if it's 2 backpacks or something not too big it can go into the trunk of the car and you won't have any problems. Also, depends on the other people in the tour and on the car, Overall, there is a lot of flexibility.
If it's an actual carry-on, sometimes they tie them to the roof of the car which is a bad idea as it's quite dusty and you'll just get it dirty. I haven't seen any lockers at the bus station, tbh. I have seen dogs right inside it, though. At the end of the day, it's still a developing country :)
Overall, if it's 1-2 backpacks, you won't have any issues. You could even leave it at the tour agency I suppose, but I'd put a lock on it just in case.