I had a similar relationship with my GC before as well, but I knew I had to get closer to her soon. So, one day, I walked up to her office and asked her if she had any time to talk. After replying that she did, I struck up a simple conversation of how my year was going so far. We ended up talking for almost the entire lunch period and now we are really close. So, all it takes sometimes is to just start up a simple conversation even if it isn’t about something you both enjoy. Most of the time, your GC will be more than happy to get close to you so it shouldn’t be too hard to get close to them. Good luck!