For example, I mention that every adult must pay a $30 application fee, pass my credit/criminal background, make a combined income of 3x the rent, and whether or not the property accepts pets.

The system protects the criminals more than the law abiding business operators.I agree with others though, turn it over to a local competent collection service. 

@Grant Jordan WardYour post (potentially) contemplates criminal trespass and felony theft. 

Wait out the criminals and bedbugs. 

Financially this deal makes sense; however, I am concerned with the safety aspect… I must live there for a year since I am looking for an FHA loan.There are areas close by that i know can have criminal activity but I am uncertain about this specific area (1-2 mile radius).

When it comes to criminal history, that is not a protected class... yet.

You could go after her on a couple fronts , small claims for breach of contract  ,criminal prosecution for bad check , and contact the new landlord as a reference after the fact .

You have to save all of your rental income to build up an emergency fund.For me I have a one-page application and we check credit and criminal record.

I also have updated my application with a section where they can address variances to my "typical qualifications," where they can explain things like an old criminal background record (still states absolutely no evictions) or a divorce that wrecked their credit score. 

This individual not only disrupted the peace of my other tenants but also engaged in criminal activities, including domestic violence and terrorizing children in the building.