Thank you for asking this question. I'm sure this question is on everyone's mind.
Unfortunately this is highly context dependent, as all the following factors play a role in the costs:
1) Which type of specialist are you seeing?
2) Which private hospital?
3) Which doctor are you seeing?
4) What is your medical condition?
A ballpark figure for specialist consultation fees in Singapore is probably about $120 - $200.
Example of specialist consultation fees in a private hospital (figures from Raffles Medical Group):
Specialist Consultant Fees
Rates
First Consultation
$146.00
Subsequent Consultation
$108.00
Extended Consultation
From $170.00
Emergency / After-Office-Hours Consultation
From $170.00
Example of specialist consultation fees in a government hospital (figures from SGH):
Specialist Consultant Fees
Rates
First Consultation
$127.33
Subsequent Consultation
$93.09
Subsidised First Consultation
$39.00
Subsidised Subsequent Consultation
$39.00