Several bike hire outlets in Brodick, SLJ. It's a long time since I hired one, but i think they're all much of a muchness. Not cheap, but will enhance your visit to the island. There is indeed a road across the centre of the island - the String Road from Brodick to Blackwaterfoot. Quite a climb, with the reward of a magic descent. Some tough climbing up the north-east of the island towards Lochranza. Take your time and enjoy it!