When you say low budget, you probably mean you don't have a car, right?
I might be wrong about this, but I seem to recall that you can ask around and people will take you in their 4x4s to different places. You agree on the price beforehand, and you sit in the back of a truck with other things they are transporting, I have read blogs about that before... However, that might be out of your comfort zone...
Here's what wikitravel says about driving your own car:
http://wikitravel.org/en/Mali#Get_inThere are several ways to get to Mali by car. From Europe one has to cross the straits of Gibraltar, Morocco, Western Sahara and Mauritania. There are no longer any problems crossing Western Sahara along the coastal road. You will need to have your car and passport information ready to hand over at the various checkpoint however. There is now tarmaced roads all the way from Europe to Nioro du Sahel (apart from 3 km at the border between Western Sahara and Mauritania). There should soon (within the next few months) be tarmac all the way to Bamako. Another option is to ship the car via a nearby seaport, for example Dakar in Senegal. There are no asphalted roads into Mali from Senegal so a 4x4 is strongly recommended. In the past the most-used road route was the asphalted road from the port of Abidjan in Ivory Coast. But since a rebellion in September 2002 the north of that country has been in rebel control. In April 2004, the road was in poor repair, and frequent rebellion roadblocks made the journey risky. Most roadblocks could be passed with good humour and a 100F CFA "present", but the dangers of unsupervised young men with automatic weapons far from authority are obvious. It is also possible to ship to Ghana and then drive up through Burkina Faso.
Here are some blogs that looked interesting:
In a car:
http://www.travelpod.com/travel-blog-entri...01860/tpod.htmlBy tour (You might want to message them and ask what company they used):
http://www.travelpod.com/travel-blog-entri...46460/tpod.html