Kamakura biking

I am spending a morning in Kamakura, specifically to see the Great Buddha and the Zeniarai Temple. I've read that there is a hiking trail that connects the two sites. Are bikes allowed on this trail? Would I be able to rent a bike at Kamakura station, bike to Zeniarai, then to the Great Buddha, and then back to the station within two hours?

Are bikes allowed on this trail?

I don't think so. Parts of the trail are narrow and steep. I think there are a few stairs here and there, too. Bikes would not be appreciated by the hikers. So, I definitely don't recommend it.

There are two more reasons against it:

1) you would require good mountain bikes, which are very difficult to find for rental in Japan

2) for your route under consideration, it does not make much sense to use these trails, in the first place

But it would be a nice idea to rent regular bicycles to visit these places, using regular roads (through attractive residential area) between the sights. If you travel at a fast pace, you could cover it in 2 hours, but I recommend to allocate 3 hours to make it more enjoyable and to account for the high possibility of getting lost. Zeniarai, in particular, is quite tricky to find with the map distributed by the Kamakura tourist desk (at least 3 years ago).

Thanks, Uji. I believe we will just hike, then, since we'd like to take the scenic trails. How long do you think it would take to hike this triangle (Kamakura station to Zeniarai to Great Buddha to Kamakura station)? Thanks again for your advice.

Here's a map:
http://www.jnto.go.jp/eng/map/prints/print_010_Kamakura.pdf
I would get off at Kita-Kamakura and hike one to Hase. Then take the Enoden line back to Kamakura. Give yourself at least 2 hours - to explore and hike. It would be about 3 km.