Yeah, give us your whole itinerary. What days you arrive/leave from Jpn, which nights you're staying in Tokyo and Kyoto, etc.

Odawara to Owakudani (via mountain train, cable car and ropeway) is 90~100min. If you're in a major rush and just want to ride the ropeway over the volcanic gorge and then do the volcano walk and hang out a bit at Owakudani, then you'll want to allow maybe 3.5 hours for Odawara back to Odawara. If you start adding in other things, such as a stop at an onsen, it will take longer obviously. Besides onsen, another thing you can do is to visit the Open Air Museum. I'm not into museums usually, but even I like that place and they have a foot onsen there.

There're tons of higaeri (day-use) onsens in Hakone, but you're really limiting choices by insisting on a private bath higaeri onsen. I'm sure there are some if you do a search. The only one that comes to mind is either the one at Fujiya Yumoto Hotel or to do the tea&room plan (rent a room for ~4hrs) at the original Fujiya (Miyanoshita) Hotel where the hot water into the room bath is real onsen. The original Fujiya Hotel, with their classy public area and nice garden, is a nice place to stop at by the way.

Whether/not you want to do plan A or plan B depends entirely on the train schedule and the rest of your itinerary. Some Hikari's stop in Odawara, but most don't. Hikari would be ideal, but otherwise it'd be the extremely slow Kodama or having to transfer once from Nozomi/Hikari to Kodama en route. The 10.32am Hikari out of Kyoto does stop at Odawara. If you do that, then you could probably do Owakudani+onsen on your Hakone swing and still make it into Tokyo around 8pm. But then one thing to worry about is luggage. Hope you don't have a big suitcase on you, because there's no guarantee a large locker is available at Odawara Sta.

Plan C might work out the best, depending on the rest of your itinerary. But then you'll have to change your hotel. Hilton Tokyo Bay is in about the most inconvenient location for doing this. If you stayed in Shinagawa, then you could leave the hotel before 8am, trek to Owakudani, spend ~1hr there, do onsen and be back at the hotel by 3pm. In fact, I've done similar before with my father-in-law on the day of his departure.