Unfortunately, your options on credit cards with category bonuses on monthly bills are severely limited. (creditcards.com)
And remember, if you have a credit card with category bonuses for shopping, you can earn even more. (upgradedpoints.com)
With a low annual fee, you can be earning at least 1.5 X on all purchases with higher earnings with category bonuses for gas and groceries. (rewardexpert.com)