Prior to covid, staying at the Conrad and area hotels I would just bring my stuff down to TLaundry and pick up next day:
https://goo.gl/maps/MFUYkcehifbmkNZN9
While they say allow 5 days, they do provide next day service for a fee (not exorbitant) if you drop off by 10am.
A pickup/delivery service I haven't used (has an app for tracking):
https://piing.com.sg
Edited to add: The last time I used TLaundry was FEB2020. The website says they are still open and it seems that they have some recent reviews on the reviews websites, so I think they are still a good option for that area.