You will usually ride with your hands on the brake levers. The curved part of the bars are called "drops" and you use that part of the bar mostly when descending. But, if you can't reach the brakes from the drops, you may need women's specific levers. In some cases, shims can be placed inside the lever to bring it in closer. With the issue you describe, I wouldn't use the drops at all, since you can't brake from there.
'02 Eddy Merckx Fuga, Selle An Atomica
'85 Eddy Merckx Professional, Selle An Atomica
'10 Soma Double Cross DC, Selle An Atomica
Slacker on wheels.