No, you do not depreciate the room or your house as an asset.
In TurboTax you would enter on the screen: Do Any of These Situations Apply to this Property?
You need to check the box, I rent out part of my home
A few screens later you can indicate "Yes" that you will let TurboTax Calculate Your Expense Deductions for You. Another question will appear on the screen that states:
Just enter the percentage of your property that was rented?
Then you can enter your rental income and enter your expenses (100% of the expense) in the Expenses section. TurboTax will allocate the amount for your itemized deductions so do not also enter them there.
Your rental percentage is the percentage of your property that you're renting out. To figure out your rental percentage, divide the square footage of the portion you're renting out by the total square footage of your property.