Are we talking about shyness INSIDE the casino or are we talking about shyness while betting? I have seen both cases in the answers. I mean shyness while gambling for real in a real casino is quite possible because there are people who would like to bet and gamble but introverts, but if you put those people in front of a pc and let them gamble you can solve the problem.
If we are talking about shyness while for example raising the stakes or something while playing online, than I don't know what to tell you. That might be characteristic and maybe you are not destined to gamble.
Shyness in gambling is good. Old gambler will never shy because they are addicted and they dont know shyness. For new gamblers shyness is good because this may cause stop them from gambling regularly and not to play anymore. Shyness and careness are two factors that can prevent you from gambling. But the problem is this that online gambling has no shyness.
I don't think shyness will make them stop from playing. If you are in physical casino and you are new, of course it's normal to feel shy but that won't stop them. They will overcome that shyness as time pass by because of addiction.