Your coworker may genuinely enjoy helping and might never ask for money, but repeatedly accepting the favor without acknowledging it can eventually feel one-sided. A simple conversation can prevent awkwardness. You could thank them for driving and offer to contribute toward gas, allowing them to decide whether they actually want payment.
If they accept, a reasonable weekly or monthly amount is often easier than calculating every trip. If they refuse money, you can still show appreciation by buying coffee or lunch occasionally, giving a fuel gift card, being ready on time, giving advance notice when you do not need a ride, and respecting days when they cannot drive you.
The goal is not to calculate every favor perfectly, but to make sure kindness never becomes something you simply expect. A free ride may not come with a bill, but it still costs the driver time, money, and effort. Recognizing that and showing genuine gratitude can keep the arrangement comfortable and fair for both people.