Me (f) and my current boyfriend have been in a relationship for 4 months now and he is expressing concerns about me being friendly with my ex. 

Me and my ex were together for 3 years. He helped me through some tough family issues and we moved country together. The relationship started to fall apart when it became apparent that we had different life styles and aspirations for the future. This was a long process and both my ex and I lived in denial for a long time before dealing with the inevitable break up. In other words, this was a peaceful end to our relationship with no hard feelings. 

The lengthy break up gave me a lot of time to think things through (Do I still have feelings for him? Would I regret leaving him? Is breaking up the right thing to do?) and I felt certain that ending the relationship was a good thing when the decision was made. I have no romantic feelings towards him anymore but I do still care about him, like you would care about a family member. 
Therefore, I am still in contact with my ex. 

My ex and I live in the same town and go to the same university, so I'm happy that we don't have that "typical" awkwardness between us like most people do towards their ex. I would however like to add that I don't think we have an unhealthy relationship either. We don't text regularly or hang out. I don't ask my friends to gossip about him and I try to stay out of his way as much as possible (societies, cafés I know he likes, pubs I know he frequents). Despite this, there is the occasional text (usually practical things like "Do you know where this thing is?" etc) and we do sometimes run into each other on the street/at the uni. I also used to play dnd with my ex and his old friends regularly, but decided to quit that as my current boyfriend found it uncomfortable.

My current boyfriend is however still finding it difficult to digest that I don't hate my ex.
What sparked this discussion recently was that my ex contacted me and said that he had bought me a Christmas gift. I was surprised that he had gotten me anything at all since we're not that close anymore but also appreciated the gesture. I didn't get anything for him in return, but agreed to meet up for a coffee so we could chat and I could pick up the gift. Haven't spoken to him since. 

I understand my boyfriend's concerns as we haven't been together for that long and as a result have not been able to build the proper trust. Furthermore, we are currently in a long-distance relationship which puts even more pressure on trusting each other. 

I don't want to ruin what we have together, but I also don't want to be a bitch towards my ex as he has done nothing wrong. 

So, I want to ask you guys. AITA here? 