No need to worry too much! While the produce in the box should ideally have been refrigerated as soon as the box was received, nothing else in there tends to be perishable, and luckily the state of the produce is rather easy to tell. If the produce seems okay to you, then feel free to use it, but if it looks like the heat got to it, it might be better to purchase replacements.
The syrups are shelf-stable and only really need to be refrigerated once they've been opened, so they'll be just fine, and the worst that the bitters might do is evaporate a bit. Everything else should be a-okay too :)