It is always easier and more informative to create related bugs from MTM than Visual Studio. It saves you time to copy and paste lot of data and save/upload attachments when you do it from VS. Plus it automatically links them all together so you won’t miss track them.
To do so, first understand the difference between test case and test result. Test results are results (success and failure) from a particular test case. TFS/MTM actually use test result to initiate a new bug. So when the bug is being created, all data related to that result (test steps, results, and attachments, etc.) will be populated to it automatically.
So, open your test result, go to the very bottom of it, select “Create new bug”, and the rest just like creating a new work item from VS.