Is there a way of sending a message to a particular user?
The only way I can see is to tag them in a question. This is good if you are wanting the discussion to be general but would not always be appropriate.
Mick
As noted at MSE, How do I contact other users?, the most reliable method is to create a chat room and use @handle to invite the other community member to it. The room is not private—others will be able to read the contents—but if privacy is a must you could at least use it to exchange other contact information.
TPTB have shown no interest in any private messaging capabilities for Stack Exchange users.