Cove is very nervous about pursing romance, in terms of the physical and emotional side. You can interpret how much is physical based on what you'd be comfortable with. But no matter what, he's never able to just like someone and start being with them. He has to go through a big process for every step.
It takes Cove until very end of summer in their last year of non-adulthood for him to finally admit that he likes the MC that way, and he almost doesn't do it. He stalls at first. And in that confession he explains how trying to change things and move forward scares him. Inviting you to the bed is him trying to be more confident and get passed that, but he ends up almost backing out again because of how strongly his own feelings impact him. He thanks the MC for waiting because you do have to wait for him to do anything. He's liked the MC for a minimum of multiple months and potentially as long as several years and is only now expressing it. Even if the MC didn't mind or really think about it, he knows he took a long time to get to it and he's self-conscious about it. I hope that makes more sense!