Sonef buscompany (just behind the stadium and the interior ministery) has a bus at 5.10 am to
Birni-N'Konni (and in to Zinder), 6500 CFA, 5 to 6 hours, from the gare routiere, about 1 km from the Sonef terminal you have shared taxis to Sokoto, 2000 CFA or 600 Naira about 2 hours. At the border you can expect a lengthy interview (it was not unfriendly an no money was asked).
Outside of Niamey, it can be a bit more difficult to find gasoline. We had serious troubles on two trips through Northern Benin. During cotton harvest, the cotton companies buy up all the available gas for their trucks. Check before you go!
The three years we lived in Niamey, we did not witness any gasoline shortages. At times, certain gas stations would be out of unleaded or deisel, but the next station would have what you needed. If desparate, there was always the option of the roadside shacks selling gasoline or oil in recycled liquor bottles. Perhaps not the cleanest fuel in the world, but it would do in a pinch if desparate.
Buses aren't a very logical way to get around in Niamey. There are very few routes. Take a taxi or share taxi instead. Once you know the prices, it's fairly easy to haggle the drivers down to the real price.
Traveling to other parts of Niger is possible by bus, but these aren't airconditioned deluxe buses. Your trips will be long, hot, and cramped. Be warned!
Cars in Niger tend to be French (Peugot and Citroen) and Mercedes Benz. Virtually all of them are imported as used cars from Europe, some maybe more "legal" than others. The Nigerien climate is hard on cars, the heat and especially sand play havoc on engines. Mechanics a very resourceful at repairing cars, especially French ones. If you are traveling in an American car, forget it. There are no parts to be hard, and the locals don't know how to work on them.