I have a home daycare and have run into this problem a couple times.
For one little girl, her grandfather used to pick her up after lunch and take her to school. I really think he enjoyed having this time with his granddaughter and also the responsibility. I know the little girl loved seeing grandpa on such a regular basis and it strengthen the bond between them and the family.
Now I have another family who needs transport to both preschool and kindergarten. Since their family does not live nearby, grandparents are not an option. Luckily, my husband is now retired and has graciously taken on the responsibility of transporting the children. This has worked out very well for all involved.
Do you have a neighbor with a child who will be in the same class as your child? Perhaps they would be able to transport your child also, even if you have to offer to pay them. If not, ask the grandparents their thoughts and see if it seems like it would be a burden. They may be glad to have the opportunity to help. You will never know unless you ask! Good Luck.