Yes, you absolutely can. In fact, it is rare when such bills are not a part of a bankruptcy. Very frequently, people will have upwards of several thousand (if not tens of thousands) in medical-related bills.
Medical bills (whether they originate from your doctor’s office or the hospital) are described as unsecured debts. Unsecured debts are debts that have no collateral attached to them. In other words, there is nothing securing the underlying amount that you owe. A secured debt (like a home mortgage or car note) does have collateral attached (like the house or the automobile). With a secured debt, if you don’t pay the monthly installment, the remedy for the creditor is to either foreclose on the loan, or repossess the car. But with an unsecured debt, the remedy for non-payment would be to call you relentlessly, and then eventually sue you for breach of contract (and once they get a judgment, they could move forward with a wage garnishment, bank levy, or lien against your house).
But these kinds of debts can be taken care of in a Missouri bankruptcy. In a St. Louis Chapter 7 bankruptcy, all unsecured debts (credit cards, medical bills, payday loans, etc.) are discharged. This means that the creditor can never again demand payment from you, call you, or anyway attempt to collect on the debt ever again; and you will never again be obligated on the debt, to either make any further payments or answer the creditor’s questions. It simply goes away for good.