With Bakelite, and many other repairs, I'm a big fan of using a 2-part slow-to-medium cure epoxy... it's much stronger ultimately than super glue, and it gives plenty of working time to get things perfectly lined up. Further, any excess can easily be cleaned up with alcohol (or acetone) before before it's fully cured, meaning any glue that oozes out can rapidly be cleaned up, making the repair even more invisible. Super glue will work on Bakelite, but your work time is virtually zero, and any excess that gets on the part or appears at the join is difficult to remove. Also, if you have to stop and start over, the superglue will be next to impossible to remove, whereas the epoxy can be 100% removed prior to cure. You can also get archival-quality epoxies that won't yellow over time (like HXTAL NYL-1). Finally, epoxy can be combined with linen or other thin fabric to make a built-up patch in a hidden area at the join that can make the part even stronger.
One trick I use is to employ modeling clay to hold the pieces in the proper position during the cure. You can also use electrical tape, which has a bit of stretch to it, to hole the join tight during cure.