Can I deduct teaching materials for teaching a Bible Study Class at church, and if so, is there a limit on how much is deductible?

If you are a volunteer teacher, you may deduct your out of pocket  expenses as a charitable contribution. This assumes that the books  and DVDs, become property of the church.   In TurboTax, enter as a cash deduction.  This assumes you purchased the items specifically for the purpose of donating them to the church.   Items that you were previously, would be treated as  the donation of used items and not as cash. 

If you keep ownership, you cannot deduct the cost for just loaning your personal items to the church.  Your mileage is deductible if you are making a special trip to teach the class.  You may not deduct the mileage if the class is just part of your Sunday morning attendance. 

Charitable contributions are an itemized deduction, essentially with no limit.  For 2020 only (Covid rules) an up to $300 cash deduction is allowed for those who use the standard deduction (non cash mileage would not be eligible). 

If you are donating items to the church, I would call that an item donation rather than a money donation.  (Donating DVDs or workbooks would be an item donation.  Spending money at the copy center to make copies of a handout would be an out of pocket expense that you can records as a money donation.)

In either case, you need proof from the church that you made these donations; a simple letter like "thank you for teaching the Bible study and providing materials" would be sufficient.  The letter does not have to cite a dollar value, you provide proof of that separately.

Note that it is not deductible to donate items to specific people, even if it is for a charitable purpose.  So it is doubly important in this case to have acknowledgment from the church that you provided the Bible study on behalf of the church, and that if the other members of the study received books or study materials paid for by you, it must be that you donated the materials to the church, which provided them to the attendees.  

As previously stated, you can only deduct items that become property of the church (including items passed on to attendees).  You can't take a deduction for the loan of materials (DVDs that you own and keep after the class.). You can deduct mileage driven when performing service for a registered charity or exempt organization.  

The CARES act create a special $300 deduction for donations to charity that does not require itemizing deductions on schedule A, but this only applies to money donations (cash, check, credit card).  Item donations must be listed on schedule A, and you will only benefit to the extent that your itemized deductions are more than your standard deduction.  There is no upper limit to charitable contributions, although if you make very large donations that exceed a certain percentage of your income, you may have to deduct the donation over several years.