I too, have a kindergartner who is dropped off/picked up at daycare. My husband used to be a bus driver. Honestly, there is not really anything you can do. The time varies because of different variables. Sometimes there is a child missing, so your child may get there earlier, sometimes there is a bus malfunction, a new driver, traffic, etc. Last Friday, my son, who usually gets dropped off between 3:40 and 4pm, did not show up until 4:45. The regular bus driver called out sick, and the "cover" driver, was lost. Transportation called and let me know of the situation, the driver himself called me, and he was not going to leave my son anywhere until he knew he was safe.
Where my son is, they dont wait outside for 20 min..they just watch out for the bus. Have the daycare provider get to know the regular driver, as it helps immensely. My son gets dropped off on the side entrance, because that is preferable to the daycare.