Yes, ClinicalBid has an internal messaging system. You can access it using the Inbox button on the main menu.
Once you are in the Inbox view, to send a new message, click on the green Pencil & Paper icon to open a new messaging window. In the new messaging window you can search for other users by name and then send them a new message. The message thread will then be shown in the left-hand menu so that you can keep track of your conversations.