...will it just naturally go through the dormant phase and then come out and resume growing? I'm thinking inside, lots of light, yearly temperature extremes 67-76.
It depends on the variety, many of the large flowering Hippeastrum hybrids are evergreen and must be forced into dormancy.
Dormancy isn't needed for the bulbs to bloom, only to ensure they bloom at a certain time!
Just like Josh says, if you're not particular when the bulb blooms again, grow it as a houseplant..just give it a little less water during the shorter days of winter and you should be fine. It will bloom again, when it feels like it and surprise you!!