How does halving a bread recipe impact rising time?
What to do

A dough should be generally risen by size anyway, not by time. But it is also very forgiving, so it will probably still give you decent edible bread if you do it by time. 

The best way is to wait until it has doubled, no matter what the clock shows. But you insist on going by the clock, don't change the time, wait the 30 minutes. It may be underproofed (with such a short time given by the recipe, there is virtually no chance of overproofing it), but the same would have happened if you were using the original amounts and going by the clock. 

Dough proofing and time

The rising time for dough at room temperature is not affected by recipe scaling, the time it takes a specific dough to double will be the same regardless of the size of your batch. If the temperature in your proofing container is significantly different from the dough temperature, you will see some effect on rising times with different batch sizes and dough shapes, as the center of the dough will need some time to get to the same temperature as the proofing container, and warmer dough rises quicker than cold dough. This is unlikely to have a measurable effect at dough amounts used by home bakers, especially considering that the possible proofing temperature window is rather narrow.