By Bus -- Unless you ask to stop at the Badawiya, the bus stops on the side of the road in the middle of town. You will then have to walk back to the Badawiya. There are two buses a day in both directions, and in theory they run to Dakhla at 2pm and 6pm, and to Bahareya around 10am and 5pm. Tickets are LE27 ($4.90/£2.50) and LE20 ($3.60/£1.85), respectively, and can be purchased from the driver. Times and prices, however, are subject to desert vagaries, and it's absolutely necessary to check the day before if you want to avoid a long, and quite possibly fruitless, wait.
By Car -- The only way to get around the oasis is to hire a local car and driver by the hour or day. Ask at your hotel -- there are plenty of both around. Expect to pay about LE250 to LE300 ($45-$55/£23-£28) for the day.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.