This is an issue every 2005 Honda Civic Hybrid owner should consider (years '03 and '04 also, I think) because sooner or later, it's liable to affect you. At 80,000 miles, a slight grinding noise started coming from the engine compartment that got worse over time. Since the car is so quiet when idling, it's was fairly easy to hear early on. I hoped it was just a worn bearing, and continued to drive the car for several thousand more miles while I considered what to do about it. Dealership wanted thousands to replace everything that could be causing it.

During one particularly long (unavoidable) trip, the noise started getting louder and more intermittent. Finally, just as I made it back to the house, the engine accessory belt broke.
The AC pulley bearing had pretty much disintegrated, and the pulley inside face became the new bearing race, damaging it in the process. The clutch coil insulation appeared to be burned, probably from friction heat. Will likely need a new pulley, but now I understand what happened.

If you catch this early, you can save yourself some money and effort. The bearing can be found for under $40. Replacing it can be done without removing the AC compressor from the car by removing the front passenger-side wheel and a couple of the plastic retainers so the wheel well plastic at the front can be pushed out of the way. This gives just enough room to remove the clutch face, and after removing a snap ring (tricky), the pulley and bearing assembly. The bearing can be pressed out with care (see various youtube videos) and the new one pressed in. An experienced mechanic could do this whole job in an hour, so the total price should be $100-$200 to have a competent mechanic do it for you. If they aren't careful, they can damage the pulley, compressor, or both and cost you another thousand in repairs.

I tried the shortened bypass belt idea for now, and it seems to be working OK. The shortened belt just skips going around the AC compressor pulley, but is otherwise the same.
Part I used was a 39.5 inch 4 groove belt, specifically 'Drive Rite 398K4' from Advance Auto ($11). The belt tensioner ended up right in the middle, so the length was good.

I think every 2003-2005 Honda Civic Hybrid owner should consider carrying one of these short belts in case the AC compressor ever seizes, which would strand your car. You could put in the new belt on the side of the road if absolutely necessary.