Before you go buying things, first consider changing the way you grip your handlebars. Many cyclists tend to slump forward so that their wrists are bending backward when they hold the bars. Get on the bike and check this out, as you might very well be doing it without even realizing. Once you've broken that habit, make sure you are not using a "death-grip" to hold the handlebars. You only need to squeeze enough to maintain control. Many people grab the bars like they are trying to choke a kitten.

Both these bad habits can cause - and will definitely contribute to - carpal tunnel.