I would just go to where your avid projects are stored, and zip up the project you are working on.
Go to the second machine and unzip the project to it's avid projects location.
If the project already exists there, move it to a different location, or point avid to the new location of the current version.
If you are trying to open a bin from machineA, on machineB, but machine B already has a copy of that bin within the project, you are asking for trouble. You have to make sure the original is not open.
Easier way is to just copy the project over, and open it on the new box.
If there are items on machine B that are needed in machine A's project...well, now you are getting a bit hairy in what you are trying to do without a shared bin locking system.