Question: Are the buldging rules applicable in generalized linear models? Specifically, to transform the independent variables? 

I've only seen it disscused/used in OLS regression.

Thanks in advance

Answer: 
A main point about GLM is that using a link function (assuming it's not the identity link) replaces transforming the response or outcome. (Why still use the poor term "dependent variable"?) Indeed, the GLM argument here is that you get the best of both worlds, namely that predictions are on the original scale, and the need for back-transforming -- and the corrections that should imply -- is avoided. 

I don't know anywhere that this is *really* well explained. Some of the original GLM literature was written by extremely smart people for very smart people, and the rest of us have to catch up somehow. 

So, the question is not "should I transform y to ln y?" but "should I work with a log link?". 

What you might do on the RHS is not changed, as I understand it.
I am interested by the term "Bulging rule" so I try to provide my answer here.

Short answer: you can transform independent variables, but generalized linear model can do much more.

I think Bulging rule can transform y and/or x into a linear relationship, but it may not work well for multiple regression, e.g. y ~ x1 + x2 + x3 . On the other side, generalized linear model (GLM) is a flexible framework. Not only you can model a non-linear relationship between y and multiple x (x1, x2, ...), you also have better interpretations from the model.