The diode rating is for the part itself. The manufacturer states that the part is rated for 3A for each part, so you shouldn't exceed 3A. There is some judgement in this statement, meaning that you can exceed the rating without damaging the part for short periods, but not for long periods.
A bridge rectifier uses 4 of these, two of which are conducting at a time. This means that if the bridge rectifier is seeing an RMS current of 3A, then each diode is experiencing an RMS current of 1.5A. So to answer your question, yes, your rating could be considered increased over that of the individual components.
Having said that, a 2x safety margin is a good thing in power electronics. If you need 3A continuous output, I would recommend a 5A or higher diode.