The sentence is supposed to mean "I am close to the bridge".
Why is it better to use
Je suis près du pont instead of
Je suis près au pont? From my understanding,
to the, which is appropriate in this situation.
Your problem seems to be one of identification of phrases.
When you say that the reason you do not understand is that "au" means "to the" you are overlooking the following fact.
Once you recognise that, thinking about what "to the" corresponds to is meaningless because "to" alone is not translated; "close to | the" is the decomposition of that phrase and "close | to the" is wrong. Anyway, were we to translate it, what would that give? You can't say "au" means "to the" and in any case that is not true : "au" means either "to the" or "at the". Nevertheless, if you say "to the" means "au" (since it is a translation from English to French), then what is the meaning you give to "to" in English? "in the direction of, towards"?; then "au" is not proper without a verb which shows movement; since no verb of movement is used and "au" does not show movement "au" does not translate "to the"; "au" means also "at the" according to the verb ("Jean va au pont." (John is going to the bridge.), "Jean est au pont." (John is at the bridge.)); therefore you have to say "vers le" and you get "près vers le" and not "près au". ("près vers le" is also meaningless.)
You're translating literally from English, but once again the often repeated mantra about preposition is true: their uses never correlate 100% from one language to another, and might obey extremely different logics.
In the case of preposition expressing the proximity of something (let's refer to it as "A") to a place or thing "B", English often takes A as its center of reference and conceptualise the relationship between the two as a movement from A to B:
But usually, a simple preposition is used in English:
French, on the other hand, uses the same deictic center (A), but systematically conceptualises the movement as occurring from B to A:
When it comes to expressing distance, both languages agree in using from or de:
“It’s French” is the simple answer. French speakers always use “de” with certain words. Here’s a link to a fairly extensive list, together with some suggestions for learning them: https://www.frenchtoday.com/blog/french-verb-conjugation/why-french-verbs-followed-preposition-de-infinitive