You are comparing tossing the lightbulb into household waste to pretty much the worst way of properly disposing the lightbulb.

• If you aren’t sure whether they take the lightbulb, check their website or call them. No need to drive there, it’s the 2020s, not the 1920s.
• Even in places like the US there are often more convenient place to dispose of batteries and CFL bulbs, e.g. some supermarkets or mobile recycling stations.
• You don’t have to drive to the recycling station separately for each bulb/battery. Your car is big enough to handle multiple of these on one trip and I am pretty certain you have some space in your home for a box in which you can collect them.

So your question is a false dilemma, because there’s a third option: Collect these things until you have enough that it’s better for the environment to drive them to the next recycling spot than to toss them in the bin.