Is it possible for a woman to have anovulation but regular bleeding that resembles a menstrual period? how common is this?

Regular cycle is often associated with ovulation but it is not always. Anovulatory cycle is common and that explains why fertility is still problematic in women with monthly period.

Not uncommon. A woman can have anovulatory cycles mixed with ones with ovulation and not be aware of the difference. If you do not wish to be pregnant, use contraception all the time, every time. You may consider implanted contraceptive, or IUD. Practice safe sex : https://www.hopkinsmedicine.org/health/wellness-and-prevention/safer-sex-guidelines