Article 24 of the Magna Carta stipulates that "no town or person shall be forced to build bridges over rivers except those with an ancient obligation to do so." What would qualify as an "ancient obligation" in this case?

Ab antiquo in Article 23 is perhaps less "ancient" than the modern word might imply.

On the eve of the Norman Conquest (1066), the idea of public order had come to include theoretically unshakeable obligations - general obligations on everyone - for "the repair of bridges and walls and the adding to the warlike multitude". That is, to supply troops when called upon, to make sure there were useable bridges on one's land, and to maintain fortifications and defenses.

The bridge obligation has a backstory rather different than the other two mentioned there (in short, it first appears much later in sources and even then only sporadically, and there was a shift in concern over time from the building of bridges to their maintenance). What's important is that, until the middle of the eleventh century, it was a universal requirement.

But then it became a bargaining chip.

An early eleventh-century charter transferring land from the king to the queen explicitly grants the holder of the land the right not to maintain bridges, fortification, or to levy an army. Now, this is pretty clearly a very special case given the people involved (and in fact, Aethelred also frees the land from royal taxes), but it introduces the idea that general, univeral obligations are in fact something within the king's power to levy and remit.

The Normans and Angevins cultivate this innovation into a bargaining chip.

After the Conquest, with the foundation of new monasteries (i.e. major landowners) and the need for older ones to reassert their legal privileges, houses received and recorded charters as the legal document guaranteeing their existence and privileges. A lot of these charters include the freedom from building/repairing bridges - a lot of them also happen to be forgeries, or have that particular clause added. What is noteworthy for present purposes is the maturing of a belief that the king has power over the requirement of bridge construction.

When Henry I came to the throne, it was not under the most promising of military circumstances. Henry's brother Robert was challenging him for the throne and possibly looking to mount an armed invasion. Henry was a new king with no track record in an age that valued personal relationships. So how did he secure his throne? He bought the barons' loyalty - and their firepower.

The so-called Coronation Charter includes the following passage:

‘To knights who hold their lands by military service, I concede by my own gift that the lands of their demesne ploughs be quit of all gelds and from all work, so that thus relieved from such a great hardship, they provide themselves well with horses and arms, so that they are equipped and prepared to serve me and to defend my realm. (trans. Cooper)

In other words, Henry issued a blanket immunity in exchange for soldiers (and perhaps more to the point, as a way to say "Hey, Robert would make you keep it up. Aren't I better?")

Medieval law worked on cases and specifics, not generalities. So after the Coronation Charter, the requirement to build and keep up bridges was used as carrot and stick in the power balance between a king and a given lord, depending on very concrete circumstances of a specific time. The general public obligation had essentially been privatized, turned into just another tool under the power of the king. The "ancient" customs and laws to which the Magna Carta refers had less to do with the early medieval English idea of universal obligations, and more to do with the specific privileges granted and not granted during the heyday of bridge-building activity in premodern England.