The big Chatuchak weekend market in Bangkok has lots of beads. It's been quite a while since I've been to BKK so maybe someone that has been more recently can update me. In one "bead" area there was a shop with actual glass walls and Air-Con and some absolutely fantastic beads. Do yourself a favor and steer clear of the "pet market" at the other end.

http://www.tripadvisor.com/Attraction_Review-g293916-d450971-Reviews-Chatuchak_Weekend_Market-Bangkok.html

Otherwise, if you have the time to go up on the Thai Border with Burma there are a lot of beads that are dug beads from ancient sites which they bring across the river. I don't approve of this practice especially since it ruins the archaeological context and the site..but this is a reality.

These beads do find their way south to the BKK Market(s). I saw guys even sitting in chairs (no booth) selling small amounts of old beads- like the blue and white eye beads. Looked to me that if you were industrious, knowledgeable and wealthy enough you could have found plenty of great beads in Chatuchak market. We were however with a friend that lives there and who speaks Thai and other local dialects so this did help.

One area sort of near Puket- up the coast but on the East side would be Kao Sam Kaeo/ Chumphong. Many ancient beads have been found there and it should be worth checking out.

Similar articles but one has more info I think:

2012 BKK Post: http://www.bangkokpost.com/learning/learning-from-news/325165/bead-rush-in-chumphon

2012 Article BKK Post on Kao Sam Kaeo: http://www.bangkokpost.com/print/325127/

Good Luck and have a great time!

EDIT: Loose Map of where Chumphon Province is in relation to Phuket:

https://www.google.com/maps/dir/Chumphon,+Thailand/Phuket,+Thailand/@9.2390435,97.5985903,8z/data=!3m1!4b1!4m13!4m12!1m5!1m1!1s0x3056058eace858d5:0x10223bc2c364ce0!2m2!1d99.1800199!2d10.4930496!1m5!1m1!1s0x305031e2c462524f:0xe9ca9a85063dba21!2m2!1d98.3380884!2d7.9519331
Anne