I need help figuring out how to count my consulting hours and structure my billing to align with my services.

I am in transition, doing some freelance grant writing and research work while I determine a long-term career pathway. My dilemma is that I'm afraid I will scare off clients if I actually bill the time I invested. The client approved my middle-of-the-road hourly rate for grant writing, and it is time for me to send out my first bill. I think I've already invested 40 hours learning their technology, researching every single grant opportunity, coming up with strategy and action steps, presenting them with a 10-page synopsis, and re-familiarizing myself with all of the different government grant channels. However, I didn't track my time because it was so choppy dealing with kids at home from COVID, me and my kids all falling sick and having to get tested, dealing with a pending divorce in the midst of it, etc. I was a mess and moving REALLY slowly while I did this initial research, but my deliverable of an action plan was very high quality. I also don't feel like I necessarily need to bill them for my learning curve as I re-enter this field. I'd guessed I would spend about 15 hours on this phase, but it took significantly more. So, does anyone have any techniques for tracking billable hours and adjusting time spent to align with the value of the deliverable? Any suggestions for improving efficiency? This client has given me the green light to develop white papers, reach out to principal investigators at the DOE, attend online conferences, etc. In other words, I'm doing much more than just writing a grant, and learning their technology does take a significant time investment on my part. This comprehensive strategy is part of the value I offer (and could work its way into a permanent position), but I find myself afraid to actually bill for what I'm doing, especially because as with any type of sales prospecting, there's no guarantee that it will result in income to the client, or the income to them may be exactly what they end up paying me in the long run. How do I bill for my time, recognize my worth, and not scare them off? Thanks!!