Day One:
How about not using plastic bin liners?
These awesome bins come with a recycle and non-recycle compartment with separate bin bucket which can be lifted out of the bin and carried to the outside garbage bin, emptied and put back each time.
Recycling right means minimising what goes into your garbage bin. If food waste is kept separately in a small bench-top food scraps bin then your waste bin should stay relatively clean (and relatively empty), eliminating the need for a plastic bin bag.