The solution is not a dedicated bus lane in an already heavily congested road... Just because buses are good doesn't mean any solution involving buses is good. Roads are very expensive to build and maintain, and maintaining a dedicated a rarely used road alongside a heavily congested road you just made more congested isn't as simple as "bus go fast = good".
And this is a challenge wherever dedicated bus lanes have been implemented: the buses cannot travel exclusively on the bus lanes, by increasing congestion on the regular lanes, you congest all the feeder lanes. Buses get stuck in nightmare traffic trying to get into and out of the bus lane.
Improving the subway network actually reduces car traffic, fewer people will use taxis and ubers, which directly leads to fewer cars on the road, and that allows buses to operate more smoothly on shared lanes.