Best way of meeting ladyboys in Singapore would be to go to Orchard Towers
. Crazy Horse (4th floor, abt 10 lbs) and Club Romeo (abt 20 lbs). Both bars are something like the Nana Plaza bars where you can buy them a ladydrink, S$20 to S$22 or tip them about S$10 for a bot of chit chat.
If you want to go the next step, their services cost from S$200 for short time, taxi to and fro S$20 (assuming you don't stay in a hotel nearby) and short time room (2 hours) in a hotel S$20/$30.
More info on my blog. Cheers