A one-syllable word in comparative form--at least in US English--requires the addition of -er or -est.
More shy is probably used more often, but shyer is correct. I would also say the most shy, although shyest is often used as well.
I would say the opposite. In BE, shier is more common, in fact I don't think anyone would say more shy. As for the spelling, I'd say shier but since noone agrees you would be fine with either.