Krish,
I don't know about renting a van with a driver, but you can easily travel to Granada via public bus: https://www.alsa.es/en
Travel time from Seville to Granada = 3 hours.
Hopefully you've planned to stay in Granada, for at least an overnight, otherwise it would be a very long & tiring day trip from Seville.
You can buy your bus tickets 2-4 weeks in advance online, or at the bus station when you arrive to your first city in Spain.
There are different types of bus tickets. We booked the 'Supra Economy' tickets.
The buses are equipped with A/C & a WC, and the seats are very comfortable.
Hope this helps.