It sounds as if your BF has to make more of an effort to get to know him better , you say he feels hurt but if he doesnt make an effort how can either of you expect a 6 year old to do so...It is up to the adults , you and the BF.. to do the devoleping of the relation ship , your son is the child here not the BF ....
Maybe they just don't like each other. That even happens with natural parents.
I partly agree with both the above posters.I am a girlfriend and my boyfriend has a 12 year old son.I have taken his son out for bike rides, taken him to outdoor fairs etc.Some of this was choice, some of it was because his Dad works almost constantly. But I know me and SS need to do those things alone sometimes.We have a good relationship in that SS rells me his troubles and I feel I partly help and I am glad.
I also still get annoyed and wonder sometimes how close me and SS are. I am actually quite relieved when we have a weekend where we don't have SS (we in theory have him every weekend but it is me who is left alone with him and has rarely been asked if this is OK).
If this helps at all I hope so.