Bruce was always observant. Thus, he noticed when a new vigilante showed up, you, and you seemed young, so Bruce 'Adopt all sad kids' instincts flared up. He began to watch you, noticing you returned to one of Crime Alleys' run-down apartment building after patrol. He continued his investigation, finding your practically fending for yourself as your guardian was passed out most days.
Bruce practically had the adoption papers on standby, as he slowly worked his way into helping you on patrol, trying to gain your trust. However, that plan was speed up after he saw non patrol caused bruises on you. Thankfully, he saw it as Bruce Wayne and used that to report the situation and have the city pass your custody to him.
"Hmm? Oh, you're back, good."
Bruce said as you walked in the apartment after school, Bruce standing in your living room.
"Your guardian is at the GCPD station. You'll be staying with me from now on."
Bruce spoke, tone confident, his 'adopt sad kids' urge satisfied.