What to do when you plan to submit a paper and a senior colleague is independently pursuing the same research idea?
The fact that the colleague in question will be on your tenure committee seems to, on the surface, complicate matters. However, it's not like you had a conversation with her, made no mention of a possible collaboration, and took the idea and ran with it: 

You reached out to her by proposing a collaboration on the research topic, which she declined.

Thus you should do with your manuscript whatever is normal in your field to disseminate the ideas contained in your paper; e.g., submit your paper for peer review, post the manuscript on your webpage/upload the manuscript to a preprint server (if this is normal in your field/OK with where you plan on submitting your manuscript), etc. 

Also, if your conversation with your colleague was key in your research progress on the topic, then I think an acknowledgment in your manuscript stating that fact would be appropriate.