Which is the more polite way to ask for permission: 能 or 可以?
For the 'asking for permission' function, 能 is similar to 'can' and  可以/可否 is similar to 'may' in English.

Strictly speaking, 'may' is the proper word to use and is considered more polite and formal, for example "May I ask you a question" but in casual day to day speech, more and more people think replacing 'may' with 'can' and say "can I ask you a question?" is acceptable. I would still suggest you use 'may' (可以/可否) instead of 'can' (能) 

Cantonese do not use 能 or 能够 when ask for permission. We say "可以" as in "我可以問你一個問題嗎？" which is a polite way to ask. To be more polite, we would say "我可唔可以問你一個問題？" 

In Mandarin, "我可不可以問你一個問題?" (more colloquial)  or "我可否問你一個問題?" (more literary) are the more polite form compare to "我能問你一個問題嗎？"