Well, to clarify, I don't consider asking for something in any given way "begging." As where some people would consider asking with an overt amount of humility and voluntary subjugation to be begging. This is fine.
Personally I consider "begging" to be pleading after a request as if I'll relent or have changed my mind in the 30 seconds that's elapsed after I've given an answer. This is what I don't like. When I've given a firm directive, or decision, I expect it to be heeded, and I interpret repeated requests after that as something like, "How 'bout now? ... How 'bout now?" Very frustrating.
If the sub is attracted to the humiliation of begging, that humiliation can be provided in other ways by setting up parameters for how any request is made, or even for how to approach making a request or asking a question. Having your sub kiss your feet, for instance, before even being given permission to ask for something, would be an easy to start this. I'm sure you can use your imagination for other ideas as well.
This is especially effective if you occasionally deny them permission afterwards -- they've gone through some show of submissiveness to get permission to ask for something, to not even be allowed to ask anyway.