confidence intervals for interpolated values in logistic regression

Dear list,
I?m running a gam model (package mgcv) with a binary response variable (y),
and two continuous explanatory variables (x and z), plus their interaction
(x:z). I, therefore, obtain four coefficients from my model (intercept,
slope of x, slope of z and interaction coefficient).

I?m interested in obtaining the value of one of the explanatory variables
(x) for a particular level of the response variable, i.e. for a particular
probability level, and after fixing the value of the other explanatory
variable (z). Doing simple arithmetic, I can obtain the value of x that I?m
looking for, but I wonder how I can obtain a measure of error such a
confidence interval, so I can compare that value obtained from other
analogous models.

Is bootstrapping a good option or are there better alternatives? Any
practical advice/library to do so?

Thanks in advance,
David