The easiest way to get overland to Bamako is to take a bush taxi either via Kaolack, Tambacounda, Kidira/Diboli (border) to Kayes; or via Basse Sante Su, Velingara, Tambacounda, to Kayes. The train leaves Kayes to Bamako almost every day whereas the Dakar-Bamako train fdoes it twice a week. The roads are generally good. Plan 2-3 days (maybe 4) non stop.
You dont need a visa for Senegal or Gambia if you are British. Visas for Mali are available at the border for CFA5,000 (€7.50). This practise has existed for years but I'm not sure if its official or not. Maybe its better to get it in the UK.
Flights from Bamako to Paris and the UK twice a week with Air Algerie (03.2003) cost less than €350 but they may be booked out. Otherwise take Air France to Paris €500.
I think the Rough Guide to West Africa is the best guide book in English but admit I never heard of the "Bradt Travel Guide"