Hey Mark,
in the video I linked above, which shows how to cut out a Jazz Bass solid body and then how to make a Jazz Bass neck with a CNC, they show all the bits used and they give the necessary cutting parameters:
If you read the “more” link you also find a link with a downloadable description.
Regarding the length of the bit (additionally to what I said about general bit length above), here if you cut from two sides, you need a bit with a cutting part that is only half the body height of your guitar body workpiece. So if you say your workpiece/body is 45 mm thick (1.75 inches), you would take a bit with 23 mm long cutting part (0.875 inches). So if you say you can only use 6.35 mm shank bits and not thicker, it would be an advantage to be able to use the short length / general purpose bit as you avoid unnecessary deflection or bit breakage danger.
Only if you want to cut only from one side, you would need a bit with a cutting part of the full height of your body. In this case you would need a long bit. 50 mm (2 inches) cutting part on a 6.35 mm bit, that’s rather long on a thin bit, I would expect deflection and be careful with the feed, as a thin long bit can break more easily.
The bits shown above are 8 mm (approx 0.325 inches) shank bits and as you can see this works well, no need for half-inch shanks. But by cutting from two sides, they avoid cutting the hole body depth which would require an extra long bit.
Makita routers are available with 6 and 8 mm collets everywhere (except in the USA where they have imperial collets).
If you want to use half-inch shanks (12.7 mm), you would need a milling motor with an ER-20 collet (can take up to 13 mm collets)
If you are a beginner, please be aware that finding the right cutting parameters can be done by trial and error, but usually it is much faster and leads to better results more quickly if you rely on professional education information.