There isn't a fixed number of dates, but a relationship should be built on mutual trust and if you don't tell her it can only be because you don't trust her. Whether you express that mistrust as a fear of negative reaction (you don't trust her to take it well), as a desire to "protect" her (you don't trust her to be able to cope with this knowledge) or any other excuse, it still comes down to a lack of trust.
If you don't tell, you also lie by omission because you deceive her into believing that you are something other than what you really are.
As for the expressed fear of being dumped and publicly outed, I have two comments:
1 You don't have to drown in order to test the waters, and in the same way you can gauge her reactions without going al the way to full disclosure since you do not trust her to react well to the full disclosure.
2 Since you cannot trust her, she is not the right person to be your life partner