As for who to ask, try to reach out to professors who you think you've stood out to during the course(s). This can be hard but it'll make for a great LOR. As for how you ask them, if you're local try to catch them during office hours and ask in pers…
I don't think it can hurt to ask your old boss, especially if you were on good terms with them and are willing to do write you one.
As far as applying without, most schools require at least one...some even two minimum. Try reaching out to some oth…