@Alison11,
There isn't a way to know if guests will be responsible but some things you can do to "get a feel" for the type of guest who is inquiring about your listing is. There have been a few inquiries we received, and we opted in declining the request.
My first thought is Airbnb is built on trusting and good communication. With that said, you have to look at what impression you are giving off to potential guests.
I recommend you add a profile description, add additional verifications, and add a profile picture of yourself.
On your profile, you only have 2 verifications and the type of verifications you have are "soft" verifications. Basically, phone numbers and emails are disposable. This sort of anonymity may attract the type of guest you don't want staying in your home. This is the first impression you give guests. You don't have to put your life story out there but sharing the type of person you are- may help quality guests feel more comfortable in reaching out to you. Does this make sense?
It is very important to ask questions during the inquiry. What is their purpose of their trip (business, leisure, combination), have they been to your area before or will this be their first time, do they have specific plans while visiting your town etc. Their responses should give you a sense of the guest.
You can also ask for the relationship between the guests and their ages, for example are they couples, friends, family etc. You can require they provide the full names of each guest and even present their Driver's License at check-in or in advance so you know exactly who is staying in your listing.
Hope this helps.