You can recycle plastic bags

From Republic Services

Contrary to what you may think, you can recycle plastic bags.

Part of a category known as "plastic film," which applies to all thin plastic bags and wraps, they can be recycled.

The issue is with individual pieces or bags and the damage it does to the recycling equipment.

According to Recology (Shoreline) 

While the plastic itself is surely recyclable, bags cause major problems for recycling facility machinery. If a plastic bag enters the facility solo, the soft, flexible plastic is easily caught in the disks and grooves meant to help sort materials, eventually causing the machinery to jam and the forcing the facility to halt processing. Because of these complications, single plastic bags should NOT be placed in the recycling bin.

Both Recology and Republic (Lake Forest Park, Kenmore) say that the answer is saving up your plastic film and bundling it into one bag.

Bag plastic bags inside a larger plastic bag, tying the top to secure the bundle, before tossing it in their blue recycle bin. This bundle of bagged bags helps the material to take on a more three dimensional shape, making it less likely to get caught in the machinery.