How do I get my boyfriend to trust me?

My boyfriend is a 20 yo male and I am a 19 yo female. Recently, he has been bringing up in conversations that my response times to his texts are slow. The truth of the matter is that I am not much of a texter and I find the pressure of responding to texts to be quite overwhelming. I tend to overthink my text responses and I would much rather communicate over the phone. I have not really explained this to him in great detail though. 

Recently my boyfriend made a comment that makes me believe he does not trust me. He said "You took like an hour to respond to my text. You are probably talking to that other guy." The guy he is referring to is my high school friend who I keep streaks with on Snapchat. I did not know what to say in the moment of him making this comment and initially kind of glossed over it, however, as I was thinking about it, I began to realize how his comment most likely came from a place of him lacking trust in me. He really does not have anything to worry about though as this guy is only a high school friend and nothing more. 

What are some ways I can get my boyfriend to trust me? How should I go about this situation?