Dont expect any bars, or clubs, or even restaurants. Just tiny shacks that sell food and household items. But if you walk around this island, you will get a whiff of what zanzibar used to be before the tourists flocked to this place.
The flora and fauna are amazing, and the beaches are beautiful. The place is conservative, so please dress accordingly, and take care to nod your head and greet every one.
The main road in Zanzibar goes from Stone Town to Kizimkazi. Kitogani is on the way. Get down in Kitogani, and then move west toward Uzi. I would strongly recommend using a Land Rover because the road through the mangroves is quite bumpy.
Or you can take the local transport or matatu till the Kitogani intersection and then bicycle toward Uzi. You will have to walk when you reach the mangroves. Carry water, because you will sweat like a pig :)
There are no buses or public transportation, to the best of my knowledge.
The people of Uzi are quite old fashioned. If you are passing by a group of local people sitting under a tree, please greet them first. A simple Shikamoo or Mambo will generate a lot of good will. Also, please dress conservatively, which can be quite difficult in the heat. Lastly, if you are a man, please refrain from shaking hands with the women unless they put their hands out first.
The important thing to realize is that Uzi is not Stone Town.