The current rating is for any one diode, as far as the junction's capability.
But in a bridge rectifier, the diodes are on in alternating pairs, so heat is generated from two diodes. The package might not actually be able to dissipate the heat even though the diodes have the current rating. Both parameters have to be considered.
Careful if you have a capacitive load, the current waveform is not sinusoidal at all. But the rectifier's datasheet usually assumes 50/60Hz sine loads for the ratings.
On power up there is a surge for many cycles until a filter capacitor charges up.