Here's my question; My mother has just recently passed away, her Estate is worth 42,000.. Can't get Bond Ins for the Estate because of weak credit, so now what? There is no outstanding debt that I am aware of that my mother owes to any creditor, so why do I need Bond Ins?

It is a legal requirement by your state. Talk to someone in the probate court and see what they say. If you are unable to get the bond, then someone else will administer the estate. Sounds as though your Mother did not have a last will and testament; is that correct?