“Unable to switch servers at this time. Team explorer is busy.”

Did a couple of things to try and resolve this.

In VisualStudio, Tools > Options > Source Control :

...but I think this is what fixed it...

From the ‘Team Explorer’ Tree, click on the ‘Add Existing Team Project’ icon, then the ‘Servers...’ button:

Remove the server and then re-add it.

Shut down VS and re-start just for good measure.