It's present perfect.
Although this phrase looks the same as a present perfect continuous (for example, "I've been waiting"), the structure is different. The present perfect continuous is composed of have/has been + present participle*, while "I've been camping" is composed of have/has been + gerund.
The name of the activity is 'go camping', and only the 'go' part of this expression changes. The word 'camping' is not part of the verb, so it does not change:
Present simple: I go camping every summer
Past simple: I went camping last summer
Present perfect: I've never been camping (before now)
Past perfect: I'd never been camping (before then)
*Edited.