This is the set-up I have found best a game I call Bike Path Polo. With the broom and dust pan you can still stop to get the glass. By adding the trailer, tote and tongs (I don't know if you can see the red hadled collapsable spring reach tongs - to the left of the Polish Eagle sticker) I can pick up trash while rolling! It works best with the wheel set as a fixed gear, and takes some getting used to so you can deposit without looking back.
The pictured trash was collected on on an 8 mile ride from Seward to Roseville. It's not all the trash I saw that day, it's just the stuff I could grab while riding.

Where the Polish Eagle leads me...

Minneapolis has a lot of bike paths. Glass happens. At first I would get frustrated when I saw broken glass on the bike path. Then one day I saw people with brooms, then there was a light bulb in my head - and not a broken one.
From that point forward my thinking changed. I had a new bike path mantra, "I have never seen more broken glass, than happy people on the bike path." Happy People win! Mechanically more slowly I added a broom rack to my bike, on a trip to Ax-man I found the perfect garbage can. With that my bike, The Polish Eagle, was ready to pick up glass.
It started to feel like bird watching, a passive distrattion on my rides. I started a mental tally of what species of glass was on the path - miller lite, a flask of vodka... There were a lot of cans, I started to pick them up too, a secondary tally of cans vs. bottles started in my head. I started to notice if I road early on Saturday and Sunday a lot of the bottles weren't broken, started to speculate - those who drink and leave bottles may not be the bottle breakers?