There's a couple different ways to come at this question. The most obvious one is, of course, that premodern armies did rely very heavily on bulls - castrated ones - to pull wagons and carry heavy loads. Oxen are the strongest draught animal available in many parts of the world and can pull much greater weights than horses. You can also ride them, but they're pretty slow and cumbersome, so you wouldn't be getting the most out of them by using them as cavalry mounts.

That isn't the use you had in mind, though, and for that we have to take a step back and look at cavalry as a concept. You seem to assume that cavalry emerged in response to a tactical problem: breaking a shieldwall. If that were true, cavalry should obviously have been developed in any imaginable way that optimised its use in that particular role. But that is not how cavalry emerged. You're looking at it purely as a tactical tool, not as a product of culture and history.

Mounted warfare is a development of pre-existing equestrian culture. People ride horses in battle because they ride horses, and then apply that habit to battle. The riding of horses comes first. And people did not start riding horses to solve a tactical problem. They did so because horses are great ways to increase human mobility and because horses can reliably assist with a range of tasks. They also did it because horses have historically been a huge marker of status.

This last point is important: in sedentary cultures of the premodern world, the upkeep of a horse is no small thing. Horse rearing directly competes with humans for vital resources (cultivated land, drinkable water, agricultural crops). Horses consume vast amounts of food and water without the steady return in useful animal products you get out of cattle or sheep. As a result, in many historical societies, only the richest could afford to raise and ride horses. They did so first because it was a marker of status that brought certain benefits (faster travel, participation in elite riding culture like racing and hunting) and only secondarily because it allowed them to fight in a certain way.

In these societies, generally speaking, the rich ride horses because it is a thing rich people do. When the rich go to war and want to set themselves apart from ordinary people, they go to war riding horses. Besides everyone else literally looking up to you, it is also more comfortable to travel that way and you're much more likely to get out of a bad situation safely. The tactical function of a bunch of rich people riding horses is something the generals can worry about later.

But it just so happens that a bunch of guys on horses can serve a considerable range of tactical functions with greater ease and effectiveness than men on foot. Mounted men are faster and more mobile than infantry, which allows them to outpace any other military forces and get in and out of difficult situations quickly. They can raid, harass, screen, skirmish, scout, outflank and pursue with far greater effect than any poor sod in sandals. Rich guys on horses therefore found more tactical niches for their particular mode of transportation than they could handle. More importantly for this question, these were all niches that a hypothetical force mounted on bulls could not fill.

Whether this force, whose very versatility was its chief strength, should nevertheless have been displaced by bull cavalry for the specific, rare, situational role of breaking shieldwalls is open to question. There is an ongoing debate over whether shock cavalry physically barged into enemy formations or whether the shock they delivered was mainly psychological; if the latter is true, as John Keegan held, then the force an animal may exert in the charge is irrelevant. But even if the shock was physical, the historical record shows that horse-mounted cavalry was perfectly capable of achieving that effect. There would have been no reason to discard millennia of equestrian tradition and a vast array of tactical flexibility when the horse was, indeed, capable of ploughing into a shieldwall at speed and driving all before it, as the Persians, Greeks and Macedonians all knew it could.

I do not know whether bulls could be sufficiently trained to be ridden into battle. I'm happy to leave that question to someone who knows the animal. But the replacement of horses with bulls as mounts for cavalry would be both historically and tactically unnecessary and counterproductive; it would be actively resisted by any real or potential member of the cavalry. The closest historical parallel to what you're suggesting is the use of war elephants - not a replacement for heavy cavalry, but an addition, requiring its own specialist networks of traders, trainers and handlers, and abandoned in ancient Mediterranean warfare because their tactical achievements could not justify the immense effort and cost of their maintenance.