Welcome to the forum. The 45* bit is usually called a chamfer bit. It also comes in other angles. Most have a bearing on the tip but you want one without. You can remove them and grind off any projection. Try searching the major bit makers like Freud, Cmt, Whiteside, and Amana. They have the largest selections and all have online catalogs.
Whiteside will also custom make you a bit to your specs, for a price of course. One other option is to use a mouldings head on a table saw. Corob Cutter could grind you a set of cutters that would allow you to make the profile in one (the custom Whiteside bit would too). The problem with most stock chamfer router bits is that they will be too wide so look at the bit specs carefully.
Someone I consider a master woodworker once told me that a master woodworker is not someone who never makes mistakes. He is someone who is able to cover them up so that no one can tell.