That's awesome, I wish you the best of luck :)

Firstly, I should say, that depending on what your definition of "witty" is, you might be focusing on the symptom, rather than the cause. The appearance of wittiness, is fundamentally linked to an advanced ability to listen carefully to what is happening right now, both in your physical/social/(other domain) surroundings, and within your own mind/body. The ability to do all this is itself much more fundamentally important than I first realized when I started improv -- which I should mention, I also started because I wanted to be wittier :)

In essence, I would recommend that if you are looking to have a witty comment, you first focus on really learning to listen carefully and pay attention to what is happening right now. The skill of observation. You will notice some people in your class are not as good at listening. Perhaps you will offer a concept, and it is totally forgotten with the next sentence they say. Notice that these people always seem to be thinking of things ahead of time, rather than listening truly to what their partner just said, or was trying to convey with their body language. These people will not be able to make good scenes, because a "good scene" has created a temporary universe which -- even if it has ridiculous laws -- is internally consistent. If you are not listening you will miss when these laws & state are established, and you will cause contradictions in the universe you're making. If this happens the audience will be completely thrown off, and will find the scene distasteful, though they may not know why. The audience LOVES to see you care about made-up details of the universe.

I could ramble on about the subject... email me if you're interested in talking about it further... but here are a few other tips:

- Learn to agree with others. The best improvisers I know will agree with even the silliest of premises. Denial kills scenes.
This is the fundamental rule.

- Learn to add details.

- Learn that not every sentence needs to be funny. The humor comes from the building of the self-consistent universe. I promise you will get the opportunity to say "the funny, laugh-getting line" eventually, if you build a self-consistent universe, and you and your partner care about its details.

- Be okay with silence, on that same note.

- Make bold character choices, but again, make your character have a believable internal consistency within the rules of your universe

- Anything is possible in the universe of the scene -- but once a "law" or "truth" has been established, you cannot re-establish it.

- The previous rule does not mean that your character and universe cannot grow and change -- character growth is something to be desired -- but there must be a reason in the universe for the change to have come about. Again, internal consistency.

- Do not worry if it takes some time to come up with a response. It is more important to prioritize listening and fully understanding what has been communicated by your partner, than it is to prioritize the speed of your next move. New improvisers will, almost without fail, prioritize the speed of their response over their response's quality. Don't fall into this trap.

- At the same time, don't overthink it. You can do this by making sure that you're measuring the quality of your response purely based on the fact that what you're saying is (1) listening to what your partner said, (2) saying yes to some component of what they gave you, and (3) adding some new information. That's it. If all you're trying to do is meet those three criterion, you have a very solid bedrock.

- Improv maxims and teachings can be notoriously cryptic at first; and in many ways it's still an art that is difficult to succinctly & fully communicate in English. Don't get discouraged if you don't understand your teacher, or the things I've just said... just understand that there are truths contained within each phrase

At the end of the day, the last tip is that the funniest things, the most side splitting laughs, are going to come from the "truths" about the real world you and I live in, that you can express through the scenes you create.

Anyway, sorry for the long response. I am very passionate about this subject, obviously, and I hope that some of this information can help you.