The next time you come over it might be nice if you brought something.
The statement is about a possible future event, but how can one 'brought' something in the future? Why should the past verb be used?
How about this way, what is the difference: the next time ....if you bring something?
The past tense veb form does not always refer to past time. The present tense verb form does not always refer to present time. There is no future tense in English, so both past tense verb forms and present tense verb forms are used to talk about future time. The past tense form here indicates doubt on the part of the speaker: he is not sure if "you" will ever bring something over. By contrast, using present-tense bring indicates that the speaker thinks that there is a possibility that you will bring something.
The same can be said of come. It is present tense verb form but talking about future time (the next time). It is come because the speaker thinks "your" coming over is a real possibility. The use of came, on the other hand (the next time you came over), would indicate that the speaker has some doubt that "you" will ever actually come over again.
If the speaker wants to express doubt about both events, he could use both came and brought. This would be a common thing to say. Last, if the speaker used came and bring, he is expressing doubt about the first event, but not expressing doubt about the second event. This last combination would be unusual, because if the speaker doubts you will ever come over again, he is probably not going to talk about you bringing something over as an actual possibility.
