Saving seeds: Likelihood of crossing without bagging?

[mari.beth]

I have 20 OP tomato plants in two raised beds, so my plants are not spaced far apart. Last year, I saved seeds from an Italian Heirloom plant I purchased at a local nursery. The plant I grew from those seeds seems to be an Italian Heirloom plant (same tomatoes as last year in terms of size, taste, etc.) This year, I have been reading up on saving seeds and I have been trying to bag blossoms in tulle as recommended. However, only for one plant so far (Black Cherry) has fruit formed in the bags. I grow tomatoes for myself and to share and do not sell the seeds (I did share some of the IH seeds with relatives this year), so it is not crucial that my plants don't cross; however, I would prefer to them not to. Any information about how likely cross-pollination is without a physical barrier or ideas about other ways to get blossoms to self-pollinate inside the tulle would be appreciated! (I did try shaking the bagged blossoms to try to get them to pollinate!)