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, “au” means “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 corresponds to "près de | le ", which you transform then in "près du" according to the principle of the contractions (réf.).
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:
First, there is no perfect correspondence between prepositions in different languages. So à is not always to, de is not always from, and en is not always in — even if those translations work in many contexts.
So how on earth do you know which preposition to choose when translating?
One way is to double-check relevant words in your dictionary. In this case, you would find that « près de » actually functions as a unit: it's a compound preposition. This method has the advantage of reliability, but the disadvantage of requiring memorization. (Luckily the set of prepositions is finite.)
Another way is to look for patterns. In this case the question to ask is: "How do we express distance from a reference point?" In English, we're inconsistent: you are "close to" something yet "far from" it. In French, these are more consistent: you are « près de » or « loin de ». You are also « proche de » or « à une distance de ». If you're beside the CN Tower, you're « à côté de » the CN Tower.
So that can be a clue. This method has the opposite advantage of not requiring you to look things up, as well as the opposite disadvantage that it's not always reliable. For example, the pattern "How do we express one thing being inside another?" varies widely between dans, en, and à l'intérieur de, whereas English is almost always happy to say in.
You will never encounter « près au » (wrong), but always « près de ».
Think "près de" as "near from", because this is the way Frenchies think it, whilst an native English speaker would use "close to" or "near to".
This question illustrates the opposite difficulty for a non-native English speaker: https://ell.stackexchange.com/questions/106192/could-it-be-correct-to-say-near-from
We use "près de l'..." when the following noun begins with a vowel: - près de l'arbre - près de l'église - près de l'igloo - près de l'opéra
“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