When using Start-BitsTransfer, the -Credential parameter is ignored. This means that you cannot access file shares that require different permissions from the currently logged on user.
Also, using the runas command to open up a new PowerShell prompt to use different credentials, and then running Start-BitsTransfer does not work.
More thorough information and several different reproduction steps is listed in the answer on:
This is an extension of the similar issue documented in feedback id: 810753 (https://connect.microsoft.com/PowerShell/feedback/details/810753/)