Environmental chemist here (although drinking water is not my area of expertise, so feel free to ignore me if you want)
Can you describe the terrible taste? Are you concerned only about taste or are you concerned about pathogens/metals?
I would personally not use RO if it was only a taste issue (you are also removing beneficial ions like Ca and Mg). I suspect you will get used to the taste (as a city guy, I find that well water taste terrible when I visit rural friends).
If you are concerned about pathogens and metals (not taste), then an in line filter (like for the fridge or on your tap) will be fine.
RO systems are about 25% efficient in terms of water wasted. Without knowing how your water is billed (e.g. most of my water bill isn't the water usage, it is the fees for infrastructure improvement, so if my water usage went up 50% my bill might only go up 10%), I can't tell you how big of an impact that would have on your bill, but you can probably do some calculations based on your bill structure. One way to look at that would be if it raises your bill $X per month, is that worth it to you to remove that taste?
If you do go the RO route, I think you'd want an under the sink RO system (not a whole house system) because you wouldn't want to waste water for showers/laundry etc.
A final concern would be environmental in nature (and maybe you don't care about this). I think Charlotte gets it's water from a lake/reservoir. It water levels are ever an issue (i.e during droughts), you might want to consider how you feel about wasting water for your RO system.