Bulletin boards indeed seem to be the best option, if you don’t already know people who might be willing to share their plane with you.
I however feel that finding a good partner is harder than it sounds. While there are certainly some exceptions, particularly in areas in which renting or clubs are no viable options, I feel that quite a few of those who are seeking partnerships are people who are actually nowhere close to being able to afford planes themselves. Or people who can’t afford to rent a 152, but who are seriously convinced that a partnership with one or two other pilots will allow them to fly a fancy plane for significantly lower costs than the $89 the local flight school charges for their ‘uncool’ 152.
It is not unheard of that partnerships came to a sudden end when the engine needed an overhaul, while the partners were unable to come up with the necessary funds. Topics like whether to upgrade the avionics, paint or glass or how to care for the plane in general also seem to be good reasons for heated discussions, particularly if some of the partners are hard-pressed for money. One might, for example, want to replace the failed transponder with a new ADS-B out compliant one, whereas the other partners just want to get a used one.
Personally, I also wouldn’t feel comfortable about buying a plane in a partnership, which I couldn’t afford alone, in case things start going sideways with the partners.
My wife and I are cheap and therefore initially thought about looking for a partner for our plane. We completely dropped this idea, for the reasons above.