Begin by making sure you have a well-developed concept of the sound you want on the bassoon. This sense can be sharpened by listening to recordings and attending performances and making notes on the positive aspects in the bassoonists' sounds that you observe.
Trying other players' instruments is also helpful. Form an idea of the ideal type of resistance and response you want from an instrument. Even instruments of the same make and model can vary widely in this area. Also, do you want a sound that is more focused than what you presently have or more broad and round?
Get feedback from colleagues and teachers. Remember your self-criticism from listening to past recordings of yourself. What tendencies do you have when you hear your recorded sound from year to year?
After drawing some conclusions from the above you should feel you are ready to start looking for an instrument. Things to bring to the trial are different reeds and bocals, a trustworthy friend and a tuner. Make sure you choose a good acoustic space for listening and playing.
When trying an instrument, always trust your first impression. It is best to gravitate towards instruments that are immediately easy to play and get the kind of sound you want. Don't think of a new instrument as a "project" that you must adopt in order to change your playing. Your playing will change consciously and unconsciously after moving to a different instrument, but don't force the issue.
The new instrument should have a pleasant resistance to it and be fairly easy to blow. It should be easy to find the center of notes, especially the "good" notes in the middle register. Try to find the "ring" in the tone.
An excellent article on how to play the bassoon from the standpoint of getting the most resonance from the instrument is "Breathe, Don't Blow", by C. Robert Reinert and Alan Goodman
(The Double Reed, Vol. 21.3 http://www.idrs.org/www.idrs/publications2/DR2/DR21.3/115breathe.pdf)
The bassoon should be easy on the hands, the keys where you expect them to be and generally user friendly. All manufacturers make bassoons for different kinds of customers. There is a model out there that is comfortable for you.
When trying the instrument, try to become aware of the "Feel vs. Feedback" or work vs. outcome ratio. This is where your friendly listener comes in handy. Since we can never have a true sense ourselves of how we sound, it can be confusing to try a new instrument. Many of the newer bassoons are harder to blow and give the player an often false sense of a more projecting tone due to the amount of work necessary to start the tone. Physical effort and resulting resonance are not always directly related. Try to find the instrument that offers the maximum resonance and good tone quality for the least amount of work. It should be as easy as possible to play the bassoon!
Many bassoonists have favorite melodies, scales or pieces they like to play when trying the bassoon. I like to start with a 3-octave Bb major scale, played slowly and slurred. Listen for tonal homogeneity in all three octaves. Try to notice any individual notes that stick out. Play it again with the tuner on and try to notice ranges that are generally out of tune. Play again and check every note.
Next try something for which it is nearly impossible to make unaccustomed adjustments in pitch, embouchure and breath support to get the sound you want. The opening of the third movement of the Mozart Concert or the staccato passage in the fourth movement of Berlioz Symphonie Fantastique is good examples. This gives you a nearly "blind" test on how quickly and easily the instrument resonates. Either the resonance is there or it is not. There is no middle ground here. I have rejected instruments based on this criterion alone.
Comparing the tone and pitch of normally fingered notes with their harmonic fingerings gives you a sense of the acoustical qualities of the instrument and can show you where your reedmaking might need changing if you buy the instrument. See the charts below.
Be sure to check out the tenor range as this is the range in which much of the solo and orchestral repertoire is written. Many instruments fail in this range, but can have superior middle and low registers. I can usually make up for deficiencies in the low register with reed making and embouchure, but it is hard to make up for a mediocre or poor tenor range. Try solos such as the Mozart Concerto second movement, Scheherazade or Tchaikovsky 4th Symphony, second movement for this.
If you have any reservations about the condition or quality of a new instrument, have a qualified bassoon technician check it over before buying.
Conduct the following tests making no change in embouchure or breath support for the second note in each. A sharp harmonic in most cases is normal. However, the less sharp the pitch the better in tune the "real" fingering will be. For changes in reed making, refer to Mark Eubanks' excellent booklet, Advanced Reed Making and Design. See also the Bassoon Family Fingering Companion.
For used or restored instruments all of the suggestions above apply. In addition, special attention must be brought to bear upon the condition of the instrument. "How is Your Bassoon" by L. Hugh Cooper (The Journal of the International Double Reed Society, Vol. 2, 1974 http://www.idrs.org/Publications/Journal/JNL2/how.html) is an excellent article that gives much practical advice on how to evaluate the condition of an instrument.
In addition, check for cracks in the tenons. Look to see if a tenon is out of round. Look at the pad seats. Are they chipped or cracked? Are they rough? Is there debris on them?
Check the pads themselves for the seal. Put a thin strip of cigarette paper under the pad, checking the seal at the four compass points. There should be some "grab" at all four points when the pad is depressed.
Remove the boot cap and the U-tube. Look for rot in the boot. Check to see that the wood hasn't swelled such that it chokes the bore, making it smaller in diameter at that point than the brass of the U-tube. Check the cork gasket. Is it cracked or is any cork broken off? Does any cork hang over into the bore?
Look for play in the interface of key rods and posts. Look for play in the way the joints fit in the case. Any play in these areas can make for costly repairs.
Check the seal of the bocal by stopping the large end and the pin hole with fingers and sucking air out of the smaller end. To check the suction, stop the small end with your tongue and apply some pressure against the suction by pulling the bocal tip out of the mouth with the tongue attached.
Above all, make sure a qualified bassoon technician looks the instrument over carefully before you make a decision.
In conclusion, always remember that adapting to a new instrument should not be a big change for the player. Bassoonists should try to find instruments that fit the concept of sound they want and are easy to play. There now exists enough variety in brands and models that achieving these goals should not be a difficult experience.