Is it a good idea to submit to a single-blind journal when I have no affiliation?
Well, you have the following options:


Write up and publish your article as an independent researcher. If your work is theoretical and mathematically provable then, there is a high chance that the lack of affiliation doesn't affect the way the editor approach your paper. However, if you are using a large volume of data and providing surprising results, then there is a high chance that your lack of credit (if I may assume it.) discourages the journal from publishing your work. The fact is that most of the journals cannot dig down and verify the reproducibility of large-scale analyses so their best bet is relying on the credential of institutes.
Approach a PI in a related field to review your work and see if he can provide some feedback/comments on that. You can revise your manuscript based on your mutual discussions and add some potential experiments up and then publish it together. You probably would save a huge amount of money as you can depend on their funding resources.