Rishiri & Rebun by Car or Bicycle

We will be renting a car from Sapporo to drive through to Furano, Biei, Asahikawa and then up north to Wakkanai to catch a ferry to Rishiri and Rebun.

Should we bring the car over or leave the car in Wakkanai and then navigate the islands using bicycles?

The car fares include the driver. Passengers are extra.
http://www.heartlandferry.jp/english/index2-2.html

For those car rates, you could rent a car for a few hours on the islands for less. A car is useful especially on Rebun. A car gives you the freedom to stop along the way as well as getting you to the north of the island.

If you're going mainly to hike on either island, I would park the car in Wakkanai and use the buses on either island to get to the trails and back.

Rishiri is better for bicycling and has a bicycle trail as well as the ring road around the island. A car would get you up the hills though to the 3rd or 5th stations on the mountain.

Rebun has long distances to get to the sights so a bicycle wouldn't get you too far unless you had the time.

In all cases, I recommend leaving the car behind as round trip fare for the car is expensive. Unless you're in a super small car, most are 4-5m so you'd pay Y16,000 to Y20,000 each way from Wakkanai to Kafuka (Rebun). Even though renting a car on the islands is more expensive than renting elsewhere, it's still cheaper than paying the RT ferry fares. You just have to remember that you'd also be paying for a rental car that you weren't using.