Paying the bus or a tax is the same thing for you if it's well done, but then as you said: it's more convenient, when you're in trouble one month you'll still be able to use the transport, tourists benefit from it, and last but not least, crazy poor people can have a chance to move around freely...
Because you don't get to decide whether you think it's worth it or not.
If the bus is too expensive, you can walk, or cycle, or use a car, or just not go on the journey. If the tax is too expensive, you have no recourse, you have to pay it anyway.
And "if the tax is too expensive then write to your local politician" is not an answer. Even if I'm the only person in the world who thinks the bus is too expensive, I still have the option not to use the bus. But if I'm the only person in the world who thinks the tax is too expensive, too bad, I just have to pay it.
And the reason is that you accrue benefits of a free bus system even if you never ride the bus. For instance, if you choose to drive, you'll have a lot less traffic and more parking available, and probably for a cheaper price, because the other people will be riding the bus. Better bus systems means more mobility for poorer workers, which means better quality employees in the shops you see downtown. By making it easier for poor people to get jobs, it makes it less likely for people to fall off the edge and become homeless, meaning fewer homeless people in your downtown area; which in turn means lower cost for police, health, and social services, which means lower crime / better service for you.
Now, maybe you don't care about those benefits, or maybe you don't think your taxes will achieve all those benefits. But if most of the people in your city do think that, then it's fair for them to expect you to pay your share.
Welcome to Socialism as Bernie Sanders wrongly calls us Swedes.
You pay for a "package" of benefits, you don't use all of them all of the time but on average everyone is happy.
A citizen deciding not to take the bus makes the bus less efficient in some ways too.
Moreover, consider this:
> If I'm the only person in the [city] who thinks wide streets and highways for cars are too expensive, too bad, I still have to pay it.
Streets and traffic lights and parking spaces and traffic enforcement and all the infrastructure needed for cars aren't free; your car ride into the city is being subsidized. If it's not fair for you to subsidize bus-riders, why is it fair for bus-riders to subsidize you?
Which rarely happens in my opinion.