I've done it both ways. We got Loki as a puppy and he was fully trained by about 10 months. It would have been a little sooner but he had some medical issues. By fully trained I mean he would ring his bell to go out, not wait. He was about 1.5 yrs old before he would sit and WAIT for me to come and let him out before peeing on the floor after 5 minutes
Sammy was nearly 1 yr old when we got her and not trained (same as you) It took us about 6 months to get her to the point where she was ringing the bell to go outside but still having accidents, and another 2 months or so for the pee accidents to stop. She still poops on the floor occasionally if we don't insist she go out at certain times a day (RIGHT after she eats), but we've found that blocking access to her spot inside helped tremendously. We are just very strict about not letting her roam free in the morning until she goes and then not from about 4:00pm until she goes. Sometimes that means crating her until she goes, but it's only a problem maybe once a week. We have her on a routine and she knows she needs to go or no playtime
