I have some adult bassoon beginners (some with interesting and unique challenges - like the former cellist who could not help placing the finger tips on the edges of the finger holes). I use a graded introductory book of tunes (The Young Bassoonist) which I use with all my beginners. Early on I move to Weissenborn Method (also graded but aimed much more for the mature musician - bassoonists normally start on other instruments and can be quite literate and musically capable. This resource is the bassoonists' bible and to my knowledge unmatched by any other method for any other instrument - we are so lucky!).
This combination works well with most players from junior high school to adult (though the Weissenborn needs supplementing with more graded tunes for the younger players in particular).
What is more challenging is how to teach adult beginners without talking down to them. One strategy is to say "I tell my younger students ...... It may help you to think like that". That way you are sharing the info but not dictating in what could be seen as a condescending manner.
I also set realistic expectations - kids can take 3 - 5 years to gain fluent technique - adults are the same - except for their sometimes unrealistic assumption that they will sort it quicker, like pottery or painting classes. If an adult puts in the same persistence that kids often do the results can be expected to be very similar.
I tell them of the successful adults now playing symphonies in community orchestras after 6 or 7 years patient persistence. Of course some of them have confidence issues that perhaps kids deal with better, but the sound technique goes a long way.
Christchurch New Zealand
Bassoonist / Teacher / Conductor