I'm in the same boat, bootstrapping my SaaS and about to launch. Another issue I'm facing, perhaps you too, is that LinkedIn is for me a great resource for making initial sales contacts. Problem: I've had a LinkedIn account for years, and it references all the employers I've had that last 10 years. I'd like to create a second LinkedIn profile for myself and my SaaS, but LinkedIn's usage policy apparently doesn't allow this. Unless asked, I don't want potential customers to know that I have a full-time gig and thus can't devote 100% of my working hours to the SaaS. Any suggestions?

What are customer needs likely to be, and how does that align with the part time schedule?

Will the side project support itself? I am asking because they will.

Do the day job people know?

Finally, what is the support expectation?

Assuming the answers to the harder questions are sane, tell them what you can do and exceed that expectation when you can.

Depending on the slow support impact, it may only affect sales a little.

What is that impact? Are there ways it can be marginalized?

What consideration can you put out there to sweeten the deal?

It seems to me that a support contract for even one customer might be enough for you to be able to be full time. It also seems to me that you aren't likely to get such a support contract if you tell them that you're part time - nobody pays big money for part-time support.