So after a few days of a cold, I decided that I was healed and took Jude out so we could start using our free onsen tickets. We went to Fujikan Hotel which is right on the bay overlooking a not too scenic cement breakwater. The guys at the front desk were very friendly, but the onsen was full of non-Japanese Asians who were not the most well-mannered folks. We entered to see 5 guys just kind of laying spread eagle on the floor. As much as the onsen may feel good, you are typically supposed to maintain a certain level of decency... And then the cacophony of cackling girls from the womens' side of the bath echoing off the vaulted roof was too much.
The onsen itself was quite hot, typical of the downtown Beppu area. Jude liked the lion-shaped faucet on the tub.
I guess this is a fair-to-midland example of a hotel bath. Most of these hotels had their heydey like 20 or 30 years ago so if you really want to experience a Beppu hot spring, I would recommend finding a nicer onsen-only facility.