How far is it from Paris Montparnasse to Paris St Michel? What is best method of transport… bus or taxi?
Bus and Metro will cost you the same, 1,80 euro/trip. You can buy the ticket from automated machines, in the Metro station.
Now, the best solution? Metro, most likely.
The Metro line 4 (purple line) takes you from Montparnasse to St Michel in 10 minutes. In addition, count around 10 minutes to walk in the train station to reach the Metro (the line 4 is underground, on the other side of the Montparnasse square)
The bus 96 can take you from Montparnasse to St Michel also. But traffic can be pretty bad around St Michel, in the evening (St Michel is a famous place to go out, and avenues meet there, so you may get stuck between people going home and people going out). The bus may slow down or get stuck for some time.
Same with a taxi, you're depending on the traffic. There is a taxi station on the west side of Montparnasse train station though. Hopefully it would cost you less than 10 euros.
The main drawback with public transportation is if you carry heavy bags. You may need to squeeze and push around to get on board. That may give you a taste of the Parisian reputation...
If you want to avoid all of this, you can walk, it is not that far (1,9 km says Google Maps), and you mostly need to follow the main avenues. But again, it may become a pain if you have bags with you.
The RATP journey planner says to take bus 96 from
Gare Montparnasse towards
Porte des Lilas, and get off at stop
Saint-Michel - Saint-Germain, for a total of 10 stops and 16 minutes.
The other public transport alternative is the Metro line 4 from
Montparnasse Bienvenüe towards
Porte de Clignancourt, getting off at
Saint-Michel 6 stops later, for a total time of 15 minutes. You'll have to walk a bit to get to
Montparnasse Bienvenüe from the Gare Montparnasse.