Ironically the best way to get to Timbuktu is by boat down the Niger river. First you have to find a bus to Koulikoro, 35 miles east of Bamako. Next, you hope it's the rainy season and find a boat to take you to Kabara. It should take you a mere 4 days (give or take a week) to get to Kabara. Luckily, at Kabara you're just 4 miles away from Timbuktu and a shared taxi should get you there in no time to book in to one of the two hotels in town.
But really folks, you can always catch a domestic flight on an old Russian plane (keep your fingers crossed on the landing.) Bus services from Bamako are available in the dry season for a bumpy 3 day journey.