I have 100 smithing. I need more dragon bones and dragon scales, but I can't find any dragons anywhere. Is there any way I can get them without killing dragons?
To find dragons, you need to do some main quest missions.
Killing the dragon in the tower is enough. You can also try to go to dragon stones, or do a lot of teleports to villages and towns, as dragons usually appear when you teleport (higher chance than normal to appear. but not much (not confirmed)).
You don't need to kill many dragons for the armor because one dragon gives enough materials for one equipment piece.
I don't think you can get bones without killing a dragon, but there is one place where you can get scales. On the hill north/northeast of Rorikstead, there is a shrine to Akatosh that has a few "offerings" lying around it. One of these is a dragon scale. If you leave the area and wait for 10 days, the items will all respawn, meaning it is possible to craft and upgrade a full dragonscale set before doing the Dragon Rising part of the main quest. If you have the Dawn Guard DLC you will find one dragon bone in the laboratory of Serana's mother.
The easiest way I have found to find dragons, if you haven't already, is to find the Dragon Shout Stones all over. Normally, I find a dragon at any one of them. Also if you want a weapon that will help even at your level(Mehrunes' Razor: slight (10%)* chance to instantly kill; even dragons, I've done it), go to Dawnstar and complete the mission given. You will be asked to kill him later, and after you do, Mehrune fixes his dagger and gives it to you. Just be careful, he also sends two Deadric Warriors after you.