It's worth considering this as an engineering problem .

The bridge constructed in 1973 has a span of ~1.5 km. I'm relatively certain that there isn't a single part of the bosphorus where the width is less than 1km. This width presents a significant engineering problem.

The 2nd part of the problem is that the bosphorus has for the entirety of its recorded history been of enormous importance both in strategic terms and in economic terms. What this practically means any bridge must not impact on maritme/naval traffic through the straight. The simplest answer to this challenge is to have the height of the bridge sufficiently high that ships can pass below the bridge.

Fundamentally overcoming both of these problems simultaneously was not possible through most of history. It's only with the construction of steel suspension bridges starting in the USA in the 1930s (most famously the golden gate bridge) that this type of span becomes feasable. The political decision for the bosphorus bridge was made in 1957.

I am aware that in ancient history there was a temporary pontoon type bridge across the bosphorus constructed by the Persians (and a similar one over the dardanelles) that an expert in Achaemenid history could provide more detail on. However this type of bridge would not have been suitable for the longer term given that it would block the flow of maritime traffic and therefore fail the 2nd of the problems above.