Is it appropriate to wear my ASU for walking the field during homecoming?

Yes, dang it. Just wear it correctly

you are a direct rep for the Army at this event. Show pride and wear a service dress uniform.

PV2 (Join to see), AR 671-1 Chapter 13-3 states the ASU is "considered appropriate for social or official functions off the installation, such as memorial services, funerals, weddings, inaugurals, patriotic ceremonies, and similar functions ... [or] on other appropriate occasions, as desired by the individual." So according to the regulation, it can be considered appropriate.
I love suits. The history of the suit may be of some use for you in picking your own course of action. They were first used by royalty to display status, even through the 1800s they were used to convey position or profession. After WWII, many Soldiers returning did not have any other garments, so they wore their dress uniform. It became very common see see Soldiers at formal functions wearing their dress uniform. However, after the vietnams war, the practice fell out of fashion, but the suit itself continued to be a status and professional signal. With ready-to-wear establishments bringing the suit to the masses, it became commonplace to see the suit in workplaces. Today's fashion is starting to drift away from the formal suit and given rise to 'business casual' as more commonplace. This is re-enforcing the rise of the formal suit as a status or professional symbol once again. A discerning eye can easily tell the quality of a suit by looking at it.
Back to your homecoming situation, females spend copious amounts on their outwear at functions they deem important, but males tend to downplay the same investment. Take into consideration your date's level of interest in the event. If you don't have a suit to match, the ASU, for a PV2 is the go-to. It is formal, and conveys your status or profession in a way that a normal suit that you may be able to afford can not. When in doubt, ask your date. I say ask her because as SFC Ab Abc mentioned, she picked you maybe perhaps because she likes that you are a servicemenber and is proud of your accomplishment. But, as SSgt Dan Montague, SGM Bill Frazer, SPC David S., SSG (Join to see), CW2 (Join to see), and PFC Jeffrey Herrington stated already if you chose to wear it, wear it proudly and correctly.
I think that just the fact you asked the question means you are proud of your service and do not mind wearing it as 1SG Dennis Hicks pointed out. So I would disregard any advice from people who say don't be 'that guy'. To me, in this case, 'that guy' is the one who might be a PV2, wears the ASU to homecoming to show he is better than everyone else and tells war stories from basic training. Be humble, your are a Soldier and the ASU is a reflection of who you are at this point in your life. If you feel like you are more than the uniform, wear a regular suit.