First off, I assume you have the big bike licence in your home country? Buying a big bike in Singapore can be a gamble as not everyone is able to get a full Class 2 licence to ride it in Singapore. You are good to ride on a foreign license with the entitlement for 12 months, after that you must convert.
Any idea of the make/model you want to buy?
Lots of places to buy big bikes, from Authorised Main Dealers, parallel importers, and private sales.
Authorised Main dealers mostly deal in new bikes. You get your full warranty and support. Prices are high...think $30,000+ for a >1200cc BMW for instance. Probably more for a Harley.
Parallel Importers can usually knock $5k or so off a main dealer's price for a new bike, but you only get the dealers warranty, not a manufacturers warranty. The BMW main dealer in singapore, for instance, will charge you $5000 to 'register' a parallel import bike with them if you ever want them to service it, and add 25% service charge on top! Buyer beware of parallel imports.
Somewhere like Mah Motors is a big Triumph Dealership, with a large collection of pre-owned bikes for sale too.
Mah Pte Ltd
1179 Serangoon Road
Singapore 328232
Tel: (65) 6295 6393
Fax: (65) 6295 0868
BMW: Performance Motors Ltd. 280 Kampong Arang Road. Tel: 63401819
Italian bikes: Minerva Motor Pte Ltd. 290 Lavender Street. Tel: 62984777
Harley-Davidson . 253 Alexandra Road, #01-04. Tel: 64750123
Honda: Boon Siew Singapore Pte Ltd. 75 Bukit Timah Road, #01-01. Tel: 63384762
Kwaks: Evershine Auto. 176, Sin Ming Drive, #01-21/22, Tel: 64535009, 64531237
Looi's Motor. No. 55, Kaki Bukit Road Place. Tel: 67431072 (five floors of parallel imports and 2nd hand bikes)
Suzuki: Guan Hoe Cheong Trading Co. 1110 Serangoon Road. Tel: 62923737, 6291666
Yamaha: Hong Leong Corporation Ltd. 37, Tannery House, Tannery Lane, #01-06. Tel: 67460415
For private sales, start with
http://www.singaporebikes.com/ and look at the Bike Mart there, and also check out the Garage Sale forum when other bikes are listed. Lots of threads on buying/insuring/riding in singapore there too.