Pure maths "dropout" wanting to finish MSc thesis Personal background
I'm currently in my thirties. I began my math path with self studying some of the university courses while in high school thanks to the guidance of a prolific mentor at the university ( he passed away a few years ago in a tragic accident). Then it continued a bit backwards and by the time when I entered university I started out with PhD and masters level courses in pure mathematics. Mainly because those were the interesting courses that kept my motivation high. I took the more mantatory courses towards the last years as &quot;fillers&quot;.
I was in the process of starting out with my 4th year thesis in my third year of studies (older type of Master degree) when my PhD programe application that I had good letters of recommendations for got rejected. This rejection together with becoming a bit burned out and feeling a bit of general social abstinence from the solitary nature of my self studies led me to abandon pure maths. Instead I started to study applied maths. I got into finance/insurance without a thesis where I'm working ever since with mainly mathematical modeling.
Current situation
Maths has always been my passion. I generally feel motivated by my work but there's a longing for some more of an intellectual challenge. I opened some of my old books in Algebraic Geometry during the COVID-19 quarantine and noticed how much I actually remembered from back then. This lit my spark in a way I have not experienced with my otherwise mundane work. My motivation other than the pure interest I have in the subject is that I feel that not having a thesis is a failure that I want to remedy. It will also be useful for future work prospects I believe. I don't think I will become a researcher because I don't have the time and dexterity with two kids or the brain plasticity at this age. It's a long road after all.
I'm currently self studying algebraic geometry from the &quot;bible&quot; Hartshorne amongst other books. I have a past PhD course in algebraic geometry but since it was so long ago I'm attending a masters level course in the subject. I'm also thinking that completing it will help convince potential advisors that I'm serious and that I'm not just talking.
I have enough credits from my past studies for a masters in pure mathematics. The things I lack is a thesis. Two actually, one B.Sc which is a prerequisite for a M.Sc these days.
Questions

Given my perhaps a bit unorthodox experience with mathematics and the fact that I don't have any degree. How do I approach professors and ask them to take me on to write a B.Sc thesis? I feel like my age and long hiatus might put many of them off. Normally I would probably visit them in the office and talk, but these COVID-19 times when everyone's working from home that's not possible. I don't want &quot;anyone&quot; as a supervisor because I'm not doing this only for a degree but because I see it now as my hobby. So I want to write it about a subject that I will enjoy.

When I was in the process of thinking what I want and how I asked a few professors about  supervising a M.Sc thesis (even though I don't have an actual B.Sc degree yet, I didn't know this was required) through mail. Everyone of them replied that they didn't have the time in the coming period but that I should ask professor X. Did I burn my bridges with them?

Taking a semester off from work for the B.Sc (I will take time off once I get to the M.Sc, however), is not an option and I do fine currently with studying on the side of my other obligations. I want to combine my work and writing the B.Sc thesis by planning to write most of it during the summer and some as I am on parental leave with my our newborn next year. This seems very specific and might put off many potential advisors. How do I touch on this subject in my contact?
You have a lot of advantages, actually. First, though, ignore the age issue. It isn't something you can change and time moves on no matter what you do.
You seem to have contact with appropriate academics in your field. You can probably exploit that. But, since you are a bit non-traditional, for someone to take you on they might be concerned about whether you would be a burden or not.
Let me suggest a path, though there are others, certainly. Find a project that you think has merit in your field. Write up an outline of a thesis and fill in some parts of it, such as the literature search. Include a few ideas that might be developed into theorems, but which aren't currently known (yes, hard, I know). If you can't do that much, at least name one or two &quot;threads&quot; that might be pulled.
Take that to some professor that you have contact with and ask whether they think this has promise, first, as a bachelor's thesis. If yes, then ask whether they will guide it and get you over that first hurdle. It might be that a second thesis can follow the first along the same lines. Spell out your academic needs and background as you have here. A period of burnout after intense study is pretty common and many of us will understand that and have possibly experienced it.
But the outline will show someone that you are serious and the existing personal relationship will assure someone that working with you will be relatively easy and not a waste of time.

Even if the professor doesn't normally teach at the B.Sc level, they might be willing to work with you if you make their task easy. Note that I'm assuming that the bachelors thesis is an absolute requirement that can't be avoided. If so, tackle it first, even if your paper is more advanced than would normally be required.