You could try asking at the many tailor shops located all over the main tourist areas -- Sukhumvit, Silom, Ratchadamri/Rajaprarop, etc., or if you are more adventurous, on some streets, you will find some sidewalk vendors with the manual foot-operated sewing machines. They mostly do alterations for the locals.

How to find them? Just luck when walking around. I would try the area around Pantip Plaza (the computer mall) on Petchburi Road, and across that road from Pantip, there are many small shopping malls, plazas, shops, vendors of all types. East of Pantip is the Platinum Mall, which is mostly small clothing shops. You could ask around there; I'm sure the store keepers would know.

Communicating might be a problem, but I'm sure hand signs and demonstrating what you want done would do the job. Writing down the price, etc would be helpful, and trying to figure out the timing for the job might be the most difficult.