In the case of Jason meeting Bruce and within a short period of time, being given - I would say appointed - the title of Robin, I've seen one too many arguments of people trying to relieve Bruce of any blame for Jason's death and other consequences associated with his short tenure as Robin.
I would just like to kindly remind people of three things:
Jason is a child, quite literally a ten-year-old boy. Sure, he sasses Batman and pushes against going to CPS, but realistically, what negotiating tactics are you expecting from a ten-year-old boy? There is so much responsibility put on Jason’s shoulders that doesn’t make sense to me. I think it’s because too many people connect Jason with Red Hood, but this is disingenuous thinking. Yes, he becomes the Red Hood after his death, but in his first encounter with Batman, he is a child. When Batman calls him ‘Robin,’ Jason Todd is still a child. Not liking Red Hood doesn’t give you the right to adultify Pre-Robin Jason.
Said ten-year-old boy is caught mid-crime by a vigilante who is known to punish those who break the law. There is already an existing power dynamic because of the difference in age, but now there is the added layer of potential 'prisoner and jailer' dynamic.***
Put yourself in Jason's shoes: You are offered a way out of a place renamed Crime Alley because of the amount of violence and lawlessness. If you accept the title that's given to you, you are guaranteed shelter, food, safety, and any other basic human need that has been denied to you, whether it be because of lack of funds or because you haven't had a stable adult figure in your life for a long time. The man who has offered you this title has proven to be reliable and has seen potential in you that you have lost sight of in the months you have spent barely keeping yourself alive. Basic needs aside, for the first time in your life, you are offered an adventure of a lifetime to become the boy you have seen swing in the skyline and in between Gotham's high-rise buildings. Would you also not take that chance?
*** Please don't misunderstand what I'm saying. I know that Bruce would not have thrown Jason into prison. I'm not going for angst, nor would I ever delude myself into believing he would do that. Bruce would never put any child in prison, including young Jason Todd. That's why I said potential. From Jason's point of view, he has committed a crime (prisoner) and is now expecting to be punished by Batman for said crime (jailer) whether it be juvenile detention, CPS, or per canon, a boarding school. That idea is carried throughout Jason running away from Ma Gunn and assisting Bruce in stopping the heist because he again steals tires and runs away from a facility that Batman had signed him up for.***
All of this to say:
Bruce bears responsibility for assigning the role of Robin to Jason.
Jason doesn't try to sneak into the Batcave, doesn't try to convince Batman to be his partner, he is given the role. And because Bruce does this he also is responsible - partly or fully, however you want to look at it - for Jason death. The entirety of Jason's decision to look for his biological mother is tied to Bruce benching him and thinking of taking Robin away from him completely. No, I don't think Bruce meant to tie the idea of being Robin with being adopted and provided food and shelter, but that's what happened.
