"If you have drop bars, you have several possible hand positions, and you should not stay in any one throughout an entire ride. Most people spend a lot of time with their hands on the brake hoods. Make use of the tops and drops as well. Switching from anatomic to normal bars (or vice versa) may help too.

The problem may involve more than hand position. Your bars may be too low or too far forward, putting too much weight on your hands. If that's the case, you may need a new stem. If you don't feel comfortable on the drops, your bars are probably too low.

You might also try repositioning the levers slightly on the bars, and/or adjusting the tilt of the bars for maximum comfort.

""Chainwheel"""

Another possible cause of tingling hands could be that you are locking your elbows. Try focusing on keeping your elbows relaxed and slightly bent.

You also might want to talk to the folks at the shop where you bought the bike. Ask them to put you and your bike on a trainer so they can make adjustments to try to relieve the tingling.

Carpal Tunnel Syndrome is aggravated by abducting your wrists. That is, 'breaking' or bringing your palms down towards your body, as in a 'limp wrist'. If your handle bars are too close to your saddle this might be the natural grip on your bike. But if you are conscience of not allowing yourself to get into this position you will cover this base in correcting your problem. I get tingling hands when I use my Mtn Bike if I am not careful but never on my road bike in over 30,000 miles as it is properly fit.