@Annette Radvansky In Texas - where you are - Property Management companies do not need to be "bonded" as they say. We are required to have a real estate broker's license, and use a Trust account when putting security deposits in them.
A security deposit is technically owner's funds according to the state property code. They are funds of the landlord.
When hiring a PM company to manage the home, that PM company will often insist on managing those funds and they will simply place them into a trust account. This is something you may want to inquire upon when doing your research on a PM company.
Once upon a time, we used to allow owners to hold their own security deposits.....until there were several foreclosures - owners disappeared - and tenants started coming after us, the PM company, for money that was not even ours.
After judge Ciro Rodriguez (famous flaming liberal judge here in San Antonio) told me to my face in court that the Property Manager is supposed to hold and account for those funds, we switched policies and now hold 100% of all security deposits in Trust.
Keep in mind, this is in direct contrast to the LAW - the Texas Property Code - that says those funds are the property of the Landlord. But, judges don't follow laws in JP court as they are elected officials.
To paraphrase - we have been court ordered to hold all security deposits.
Take care out there!