Dry hop mistake? Help

I may have screwed up on bottling my Dead ringer. I dry hopped without a bag in the primary and siphoned to bottling bucket. However, a lot of the dry hop pellets did not sink with the trub. I used a sanitized filter to get some of them before I moved it to the bottling bucket.

Despite the care I took in transferring to bottling bucket and then the bottles, I’m concerned I will have hops floating in my bottles.

Should the hops settle down during priming and chilling phase? If not, I was thinking I would simply filter when I pour in a glass. I’m also concerned if this will result in any contamination.

Any thoughts or suggestions are greatly appreciated.

I always dry hop my Dead Ringer with pellets in the primary without using a hop bag. I dry hop for seven days for a total primary time of four weeks. Hop particles that may be picked up by the siphon , and make it to the bottle, will settle out during the conditioning period. Just use a smooth pour under a light to watch for the sediment at the bottom of the bottle. A fast pour will suck air back into the bottle mixing the sediment that is present into the beer.

I also use a 1" × 6" bag clamped to the end of my siphon tube inside the bottling bucket. Extra insurance in case I get the siphon to close to the trub layer and pick up a lot of hop particles.

Edit: The bag is made from a fine mesh grain bag.

I never dry hop in a bag. I figure whatever gets through to the bottling bucket still has to get through the spigot and the spring in my bottle filler. Whatever is left settles in the bottle, like @flars said. It really is amazing how well the spring loaded bottle filler acts as a filter. I’m always cleaning hop leaves out of it.