Is it safe to use a bridge rectifier at (up to) its rated current, at DC?
BURNING BRIDGES.

In your solar application you dont have to worry about surge current because solar cells have a short circuit current thats not much greater than the MPPT current.  

Not using all the bridge is helpful but there are a couple of things to consider.


The thermal impedence of many of these bridges is much higher than say a TO247 package so you need a good low thermal resistance heatsink for you to get anywhere near its rating at an acceptable junction temp like 100celcius, in other words the bridge could use more space than the alternative discretes.  
The slow standard silicone diodes that appear to be the only thing available in these bridge packages can waste a little more than 1V per diode! You may want to do better by using a Mosfet or a schottky, then the heatsink issue isn't an issue and you aren't wasting expensive solar capability.