First of all, congratulations on completing your second bachelors degree online, while working, 11 years after finishing a Masters. In my opinion, this is a bigger accomplishment than might meet the eye, and certainly a bigger accomplishment than you get credit for on paper.
There is nothing wrong with asking for a letter of reference 11 years or 50 years later. However I do very much sympathize with you that it is a little bit embarrassing that you did not maintain contact for 11 years. I have had the same experience, with more than one reference writer from the past. One of them did not even reply to my email saying that I wanted to re-connect with him (I did not even ask him for a letter of reference, just wanted to meet him since I was back in town briefly); another took forever to reply but did remember me and said he was willing to help in anyway; and another one replies to me immediately every time I write to him (once was after 5 years of no contact and once was after 4 years of no contact). In every situation, I am embarrassed that I didn't stay in touch, and it takes me a long time to write to them, and I feel guilty for it afterwards.
However professors often have hundreds of former students, so you can imagine they have a wide spectrum of experiences: from people who they generously provided thousands of hours of time and love and care and resources to, who show no appreciation and never speak to them again, and even might backstab them at some point in the future; to people who stay in touch monthly by email even if they were barely acquainted.
It is not going to be the first time that this professor has been asked for a letter of reference from someone who he doesn't know very well, since we often get asked for reference letters in some of the strangest circumstances, so don't worry about that. It is also not the first time this professor has had someone not stay in touch wtih them, just think about the thousands of students he's had in the past.
The professor will probably be happy to know that you are pursuing an academic career like he recommended 11 years ago, he might be happy to see that you still remember him and considered to ask him rather than someone else, and maybe he will take the opportunity to help you (which often leads to you helping him, later down the road). It has certainly been done before, with gaps much longer than 11 years.
You probably don't want to go in right away asking for a letter of reference though.
- Get back in touch with him as soon as you can, with an email reminding him of who you are and which thesis he advised.
- Make the email personal (make sure it does not look like a copy-paste job): Tell him some of the ways in which he influenced your life, for example quotes of his that you still live by everyday.
- Update him on where you've worked, and that you did the second bachelors degree
- Tell him that you now wish to pursue the PhD just as he originally recommended, and why the recession caused you not to do it before.
- Keep it short, please !!!
The last point might seem a but surprising, considering everything I recommended for you to do. However you just need 1 or 2 sentences for each of these points. If you go into too much detail, he might feel obliged to do the same in return, and then you'll never get any reply, because it will be a reply that requires a lot of devotion on his end.
He will either not reply at all, in which case you can tell me and I can try to help you with a follow-up email. Or he will most likely reply saying that it's good to hear you are pursuing a PhD (maybe even with some advice, but don't expect too much). At that point, you may thank him for his kind words, and say that you are happy to know that he supports you, and would find it helpful if he could convey that in a short letter of reference. Make sure your emails are pristine and very polite and respectful.
There's still a good chance he will not reply or will not be helpful, but there's an even better chance that you do get some positive support/encouragement, so it is most certainly worth a try.