Step 1) If you encounter Durak(?) or whoever the Dawnguard Orc recruiter is, kill (or pickpocket) him quietly somewhere. I followed him leaving Winterhold after he spoke with me.

Step 2) Loot his crossbow and bolts.

Step 3) Now, that was easy, but here's the difficult part. You will still have to complete the Dawnguard parts up until you join Harkon, so you can use that time to find a few more bolts around the keep. After that, though, you won't have many more opportunities at bolts. The good news is that Dwarven ruins now have Dwarven bolts for you to loot. The Dwarven Spheres always drop about 11-14 bolts when they die, so that's the best way for a steady stream of bolts. The other, less reliable, way is to kill any Dawnguarders you find and loot their bolts.

Step 4?) I think there might be some NPC's with enhanced crossbows, but this might just be some of my unreliable memory.

If you have any more tips about good ways to get crossbow bolts without joining the Dawnguard, post them!

Well you can just talk with the orc and he gives you a crossbow with 40 bolts you don't have to kill him

Eh, where's the fun in that?