A commenter pointed out that Paul seems to be countering an unquoted critic in 1 Corinthians. This seems likely:
1Co 9:3 Mine answer to them that do examine me is this,
1Co 9:5 Have we not power to lead about a sister, a wife, as well as other apostles, and as the brethren of the Lord, and Cephas?
In verse 3, Paul is saying he is being examined and then begins a long list of rhetorical questions (possibly meant to answer the unnamed, unquoted examiner). Verse 5 is about female companions. Paul may be answering a critic who discredits Paul by pointing to a female traveling companion (possibly not a wife because Paul says earlier he is not married (1Co 7:8)).
It seems that Paul, not unlike Jesus (Mat 27:55), had females who would follow him during his ministry.
1 Corinthians 9:3-6 Mine answer to them that do examine >mewewewe< power to forbear working? Perhaps Barnabas was married. But I think the main thing I would take from the passage is that because Paul worked for a living and didn't take support from the church some were questioning whether or not he was a fully fledged apostle, perhaps Barnabas and his wife were being supported by the church.