The fee to file a bankruptcy case is the same throughout the United States, including in Missouri. Bankruptcy fees are set by federal law, so they don't vary by state. To file for Chapter 7 bankruptcy, you must pay a filing fee of $335. For Chapter 13 cases, the fee is $310.
If you can't afford to pay the entire fee at once, you can ask the court for permission to pay in up to four installments. In Chapter 7 cases, you can also ask the court to waive the fee altogether. This option isn't available in Chapter 13, however. You can use Chapter 13 only if you have enough monthly income to fund a Chapter 13 repayment plan. The court is unlikely to be convinced that you can afford your plan payments if you can't even cover the filing fee.
Whether you use Chapter 7 or Chapter 13, you will have to complete two counseling courses: credit counseling (before you file your case) and debtor education counseling (before you get your discharge). The accredited agencies that provide this counseling are supposed to make it available regardless of your ability to pay; typically, the fee is about $50 for each course.
If you hire an attorney to help you with your case, you'll also have to pay attorney fees. Attorney fees for bankruptcy vary considerably, depending on whether you use Chapter 7 or Chapter 13 (which is considerably more work for the attorney) and on how complicated your case is. Before you retain a lawyer, make sure you understand how the lawyer charges (by flat fee or by the hour, for example) and get an estimate of the total costs you'll be facing.