@Linkat,
I heartily dislike plastic, too, but have no need for storage bags anyway. I use glass containers for just about everything. Edgarblythe informed me about microwaving plastic so I went through my 'tupperware' storage cupboard and threw them all out.
A couple of our larger grocery stores no longer provide plastic bags (yay, it's about time) but will sell you a paper one if you forgot your cloth ones.
Can you put your silicon bags outside to dry?