Seal in two plastic bags.
You are so right in saying that the broken bulbs should never be disposed normally becasue of their mercury content. Best is to gather everything with a broom, not a vaccum cleaner and use two plastic bags to put these. You can then just keep it with other trash. Nowadays most local and state agencies have recycling options for the bulbs. You can also visit www.epa.gov/bulbrecycling for more recycling options at your locality.