Hi TJ,
I think your professor was perhaps wise in asking you what you desired in a mentor, as determining it will most likely help you to find one who is appropriate for you. But here are some suggestions.
Asking someone to mentor you is asking for a commitment of time. If you find someone suitable, recognize the cost that they bear and be willing to make yourself available to them at times and places convenient to them.
To put yourself in a position where you are willing to mentored, requires a large degree of honesty and transparency on your part. Are you willing to do this?
Find someone who is discreet, that you may have confidence in him to know that he does not readily speak of other's affairs.
Before even asking if the person would consider it, make sure that he has a prayer relationship with the Lord. It the person does not have the Lord's ear, he should not have yours.
Find someone who you recognize has both wisdom and discernment. A mentor should have some ability to look past what you are telling him, and perhaps surprise you with answers or questions that you didn't expect.
Wisdom is with aged men,
And with length of days, understanding. (Job 12:12)
In the light of the above, sometimes an older man in the church is well suited to mentoring. If he has followed the Lord faithfully through his life, he will have learned many things. Often if he is retired, he will have the time also.
A mentor shouldn't be someone who is there to provide you with all the answers, but rather is someone who can help you learn to come to the answer yourself. As an earlier post revealed, a good mentor should always point you back to Jesus as your best source. (Although he may be adept in showing you what is short-circuiting your path to your best source) :-)
Home meetings and bible studies can sometimes be a good place to determine who might fit the bill. If someone can be seen to provide thoughtful and wise answers in these settings, and has shown an ability to speak into the lives of others there, further discourse could be made with them to find out more about them. Go for coffee with them, or visit them. If the person shows regard and care towards you in this setting, or if you open up to him about some portion of your life, and you see that he responds wisely; it may be worth pursuing asking him if he is willing to mentor you. I would suggest that you try to get together with the person at least once or twice before asking him whether he is willing. This will give you time to pray about it and him. If you are truly seeking to grow in the Lord, and are willing to be mentored, don't be surprised if the Lord has already spoken to the person about it by the time you are ready to ask him.
Mentoring is a biblical principal, Paul told Timothy, "And the things that you have heard from me among many witnesses, commit these to faithful men who will be able to teach others also." (2 Tim. 2:2) A good mentor himself looks for those who will respond well to him, and will in turn be willing to pour out their life into the lives of others. If you are not willing to in turn give into the lives of others, you may be disqualified from being mentored by those with true wisdom. For their wisdom and discernment will give them the prudence to say no to you in favor of retaining the time to mentor someone who will respond. But if you are willing to grow in the Lord, and are willing to be obedient in reaching out to others yourself, I would suspect that the Lord will open a door for you.
I hope this helps you somewhat, and that the Lord will supply your every need.
Cliff.