I used to commute from Bedok reservoir to Alexandra. I used to go straight down changi road, nicol highway through Tanjong Pagar (neil road Ithink) then up the back of Henderson and delta road through the HDB's - (I tried to avoid Keppel road, cars going too fast). any way its pretty busy and difficult to avoid the traffic
The bus lanes are like superwide cycle paths and a great help to getting you through the CBD safely in light traffic. I did get pulled over by some LTA guy once who said I wasn't a public bus therefore not allowed to use the bus lanes and could be fined; but I checked with the LTA and TP and they both told me that cyclists are allowed to and should use the bus lanes so as not to obstruct traffic. Hopefully they have told all their minions this by now.