That's not the only way. We have more ways:
* use low dose of antibiotic to kill enough bacteria to let the immune system to deal with the rest. Then ensure the subject is cured until all bacteria are killed so that none escape. Low dose might be needed because most antibiotics are actually pretty harmful and the harm is managed with low dose.
* use more than one antibiotic in combination with the idea there is very little chance bacteria will gain resistance to both of them at the same time.
* use the antibiotic only as a last resort. This is especially useful for bacterias that are not very harmful normally, but might become harmful for certain subjects (for example, immunosuppressed). If a bacteria with resistance escapes, the resistance might not be very useful advantage in outside environment where people do not need any help to fight off infection or when infection can be more routinely treated with another antibiotic.
Again, these are our current strategie
I think you're misunderstanding how resistances work.
Bacteria don't "start developing" resistance, if they survive the antibiotic at all they already had resistance by stroke of luck. The surviving, resistant bacteria will subsequently survive and outnumber the dead, not-resistant bacteria and we generally call this "developing resistance", but the resistance itself is down to a simple question of whether it was already there or not.
Resistances do not come to existence after bacteria come across an antibiotic. If resistance is there, the dosage won't matter because the resistant bacteria will survive regardless.
That’s not how evolution works. A few bacteria could be resistant to low doses. After the low dose, and a short wait, now the entire population is resistant to the low dose.
That gives them a much better starting point for mutations to the resistance gene and for crossing with bacteria that have some other complimentary resistance gene.
We don't really care which of those trillions of sewer bacteria carries the pre-existing genes that resist an anti-biotic; we care when a new strain starts becoming prevalent and decreasing the effectiveness. From our perspective, it's a new resistant strain.
I think the main approach to prevent antibiotic resistance is coming up with a way to prevent bacteria ever coming across a low dose of the antibiotic. As long as we make sure the dose is either huge or zero, antibiotic resistance shouldn't evolve.
Unfortunately, humans aren't a well controlled lab experiment - and there will always be people taking a half-dose, or flushing the antibiotics down the drain where they get diluted and suddenly trillions of sewer bacteria get exposed to a low dose and suddenly start developing resistance.