It's unlikely that the charges would be dropped. The offence was against 'public order', as well as against the bar owner's property. Even if the bar owner's interests are satisfied by an apology and compensation , those of 'public order' won't be.
However any punishment might well be less if the court is told that you've apologised and paid for the damage.
If you do offer to pay for the damage it's important that your offer should be 'unconditional'. If you say "I'll pay for the damage if you ask the authorities not to proceed with the case", that would be regarded as 'attempting to pervert the course of justice', which almost always leads to a substantial prison sentence.
Chris