If you are using the MLE estimator, you can use what is called the invariance principle to estimate parameters that are functions of a particular random variable.
So lets say you use the MLE estimator for b (call it b_hat). Then if you want to get an estimator for d_hat and you use the MLE estimator to get b_hat then d_hat = f(b_hat) = 1/b_hat - 1 and you're done.
There are also ways of generating intervals for these estimators as well and you might want to get a book on statistical inference.
This is only guaranteed as far as I know for the MLE estimator so don't try and use another one like Method of Moments and do the same thing.