Best advise from the best reliable local online map here. Sometimes if you want the shortest path then you need to swim. Follow their instruction below while enjoying Singapore River.
After alighting from bus 61, then it is just a decent 321 meters walk. I am not sure how big is the river. This suggestion only costs 91 cents and no traffic jam even in this after-office peak hour !
I should write to them about this hu..hu.. However I have to check it tonight whether there is really human walkable path :-)
Yes there is Cavanagh bridge that links Raffles Place business district to this museum. The bridge is not shown in the map. O..la..la this museum is just opposite the tall UOB building, very popular place to hang around, with Raffles Place MRT on its basement.