The stage with no published clock
Mali has not joined the Hague Apostille Convention, so a British stamp on its own does not close the file and embassy legalisation is required to finish it. That final stage is handled by officials acting for Mali, and they set their own pace. It is the one part of the route you cannot estimate, and every sensible plan is shaped around that fact.
The parts that behave predictably
Everything on the British side runs to a rhythm you can work with. Edinburgh Registration Service at City Chambers, 253 High Street, Edinburgh EH1 1YP, prints certified extracts of Scottish births, marriages and deaths on a known turn. The FCDO Legalisation Office then handles the stamping by post, with no counter to visit and no queue anyone can join in person.
Two British speeds, one price each
The stamping has two lanes. Standard post costs £45 for each paper, and a next-day service open to registered businesses costs £40 for each paper. Choosing between them is a real decision at the front of the route, but it changes nothing later. An apostille from United Kingdom to Mali reaches the consular desk at the same point in the queue either way.
Where time can actually be bought
The only dependable way to buy time here is to begin sooner. Ordering the certified extract early, and moving several papers in one go rather than one at a time, lifts whole weeks out of the front of the plan. Document legalisation for Mali punishes a late start much more heavily than it punishes a modest budget.
French, and the journey south
French is the working language of official life in Mali, so an English extract usually travels with a French version alongside it. Commission that while the British envelope is already out, rather than afterwards. The last leg to Bamako is long, and a tracked service earns its price simply by telling you where a package is when a deadline is close.