Road between yellowstone and grand teton?

It's actually a surprisingly long drive from say, Old Faithful to Jackson / Jackson Hole. Mostly depending on bison delays. Something like 100 miles, but you could spend a good portion of time parked while someone twenty cars ahead stops to feed a bison.

Bison too but not Bears.

OP it is a road like any other road. It goes out the South Entrance of Yellowstone and when it ends make right turn towards Jackson, WY. The Tetons will be on your right and if you continue you will end up in Jackson.

Just exit Yellowstone NP at the South Gate and you'll enter Grand Teton NP in just a few miles. The road is highway 191.