If you are on Facebook, find the Seattle Family Biking group. Lots of good info there, and it's not limited to Seattle people.

I think the thing to start with is to educate yourself in safe riding techniques. Learn how to position yourself in the road, how to control traffic with signals and position, how to be visible with lights and so on. A local bike shop or club may be able to help you there, or check out the League of American Bicyclists.

Once you have learned about safe riding techniques, you will be a lot more comfortable helping your granddaughter ride safely with you. When I rode with my kids (the scamps are adults now and don't wanna ride with their aged parent any more, darn it) I would have them ride in front of me so I could call out to them with information about things to look out for. I also rode in back so I could guard them from cars coming from behind. A mirror was very helpful for this.

hope this helps!