Yes, that is fine. You have to understand that learners' dictionaries contain simplified definitions. The regular Oxford online dictionary has a sub-definition that covers the case of listening in on a conversation.
- Conceal a miniature microphone in (a room or telephone) in order to eavesdrop on or record someone’s conversations secretly: the telephones in the presidential palace were bugged
1.1. Record or eavesdrop on (a conversation) using a concealed microphone:
she fears that her conversations were bugged
The people at Oxford must have evidence that people do use to bug [something] in the second sense, otherwise they wouldn't have listed it. That is how they work. They work from evidence.
You personally don't have to use the word in that sense if you don't want to, of course, but I think it's a useful sense because otherwise you would have to be a bit more wordy.
That is, instead of:
They were bugging his telephone conversations.
You would have to say something like this:
They were listening in on his telephone conversations with a bug.
They were eavesdropping on his telephone conversations with a bug.