@Kebo
First off, . . . Warm welcome to IAP !!
I strongly encourage going the TBC route. . . I have been TBCing almost from the beginning of my pen-turning . . . no downside, IMHO !
I would also suggest that you do your TBCing without any bushings. . . Bushings are just an unnecessary and troublesome expense, IMHO.
A good pair of calipers . . . make frequent measurements . . . take it carefully . . . and you'll never look back at that old mandrel !!!
Oh ... you will need a live tailstock center . . . probably with 60-degree center. . . just ask at any machine tool place.
And .... you will need a parallel-sided dead center for your headstock . . . . again, probably with 60-degree cone shape . . I don't like a spur center
Sometimes we refer to this as a "drive center".
I say "parallel-sided" ( referring to the shaft of the 60-degree cone ) so that you can mount it in your headstock chuck.
If your headstock has an female MT2, you could also use a male MT2 dead center ( 60-degree cone ) without any headstock chuck.
Again, just ask at any machine tool store. . This is also a very common item.
For a drive center, I actually prefer to use a diamond cone . . . for example, this . . .