To find the number of hours \( h \) Mateo rented the bike, we can set up the equation based on the total cost of renting the bike. The total cost consists of a base charge of $13 plus $4 for each hour that the bike is rented. The total amount he paid is $37.
So we can write the equation as:
\[ 4h + 13 = 37 \]
Therefore, the correct choice is:
4h + 13 = 37.