I dont think its advisable to import one in as the bikes here (bigger CC) are relatively affordable. To bring one bike in, you would need to have custom clearance, LTA clearance etc etc etc. On top of that you would have to engage a forwarding company to ship the bike over.
On another note, if you intend to buy a bike here, you would need a valid local insurance first prior to taking the bike to the street. Of course before doing that, if you have the cash, you can just pop into any shop and tell them you wanna buy a bike. They would only need some form of identity from you, is that simple.
I would suggest you post your question on the following website, there are tonnes of other items which you may need to address, and I am sure the folks overthere can address it for you more comprehensively.
http://www.singaporebikes.com/forum/
Good luck