How do i become friends with a shy person

So I wanna befriend this guy but what I’ve noticed he’s really shy. For some context me and this guy have had classes together (mostly 1 or 2) since freshman year and have never interacted, I always seen him alone and not really talk to anyone unless they kinda ask him for something, this year is my senior year and I have him during gym and we have been playing together since almost the start of the year, we play badminton or games daily and our lockers (in the locker rooms) are close to each other (like two lockers apart) so we see each other everyday but never talk outside of very small interactions based on what we are currently playing. The whole first semester we didn’t talk outside these small interactions and this semester I really wanted to talk to him but didn’t know how, I then asked my friends that I wanted to be friends with this guy and that what should I do and they told me to just go up to him and be direct and forward like in kindergarten, I thought I was cute and with basically all of my friend kept telling me this I thought it was a good plan. About a month ago in the locker rooms I finally got courage to go up to him but I also got nervous and I started of by first asking for his instagram, he got nervous and said “why?” I then got nervous and when I do I start speaking fast and I said “oh well do you wanna be friends we play together everyday” he then started stuttering and could not really talk but I got the gist and asked him if he didn’t use instagram to which he proceeded to shake his head (in a no motion) I then said if I could have his number and in a nervous voice he said “no sorry” I just said that it was fine but then I felt bad cuz I think I might’ve made him uncomfortable. This brings me to today, from an acquaintance I found out he’s alone in the library during my lunch period and I was wondering if I should go and try to talk to him and not be so straightforward this time but at the same time if he’s alone in the library what if me going there disrupts his zone, what should I do because I feel that if I talk to him during the locker or in gym it might be a bit weird and I wanna try to approach him in the library but don’t wanna seem weird and I feel that I’m running out of time because we only have like less than 3 months of school.