I was referred to an ENT specialist in Portland, OR. I requested many
times about the consulting fees. The administrator never gave straight
answer siting it depends on the complexity, copay, etc. For 10 minutes
of worthless consultation I received a bill of $300. As it goes
towards copay, it is all on me. How would I contest it? Would it be
small claims court?

do you have insurance?  did you get a statement from your insurance
company ( despite the deductible) . if so the visit code submitted by
the doctor must accurately reflect the complexity of the visit.  the
doctor is fully accountable for the code he used ( as opposed to the
price charged).if there is a discrepancy you should ask your insurer
to intervene,  regardless of whether they had to pay any money on your
behalf.

The best course is to contact the local medical society.  Give them
the full details of what was performed and they should be able to give
you the typical charges from doctors in the same area.  I've advised
many people to do this and some have saved thousands of dollars.  That
works even when your insurance company says the doctor's charges are
higher than "reasonable and customary".