There are some tricks but won't always work for you. If you are new to road riding, try riding in your hoods and braking from your hoods for a while. I hardly ever ride in my drops unless I'm really just going on the flat straight. If your hands are closer to the middle of your bar, i.e. hoods or on the bar on the flat upper part of the bar, your bike will be more stable. Why, you ask? Because you do not have the leverage that you have when you are out on the drops - farthest from the middle.

These are all stop gap methods, but they will give you the idea of what happens when your hands are on the top of the bars, on the hoods and on the drops.

The basics of a road bike are: Keep your elbows bent, if your elbows are bent you will not affect the bike so much with your weight. Keep relaxed and stay centered on your seat or over the bike so that you do not affect the bike side to side. Keep your weight off of your arms (bend your elbows), take the weight in your core, your tummy, balance from your abs. If you are afraid to do this; go out on a quiet, wide, straight piece of road and practice keeping your elbows bent, your weight centered and controlled with your abs; take your hands off the drops, try braking from the hoods, put your hands on the flat part of the bars and then , PRACTICE, taking one hand off and signalling, etc., etc.

Pretty soon, it will be second nature, but it does take some practice.