Back when I was car-light I would simply consider my options: either I could enjoy a bike ride and not have to pay for gas, or I could endure the drudgery of sitting behind a steering wheel and spend more money...

Specific to your situation, it sounds to me like you haven't reached the point yet where going places by bike is easy - when you reach for the bike you hesitate because it involves some discomfort or extra effort. The first issue is the simplest to address: once you have good equipment (panniers or otherwise) that allow you to run errands and carry necessary items without discomfort, that will be one less thing to discourage you.

But perhaps more important is the willpower/habit aspect: riding places is tougher at first because you have to make a special effort to plan your route, schedule, equipment, etc. The good news is that once you get used to riding places, you'll be able to grab the bike and go much more easily because you'll instinctively know how long it takes to cover a given distance, what to wear, and what to expect en route. But when starting out, there's no real alternative to making a commitment to yourself that the bike will be your primary mode of travel, maybe at least three days per week to start, and as you gain experience you'll grow into being car-light and using the car only when it's actually necessary, and not because you're not comfortable riding instead.