Yes - in a multitude of ways
To see how we can prevent/stop/disrupt a readied action, let's start from it's definition:
Ready (PHB p. 193)
First, you decide what perceivable circumstance will trigger your reaction. Then, you choose the action you will take in response to that trigger. [...]
When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger. Remember that you can take only one reaction per round.
When you ready a spell, you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs. To be readied, a spell must have a casting time of 1 action, and holding onto the spell’s magic requires concentration.
So, what are the ways we can stop the readied action from happening?
Stop the trigger from happening
Obviously, this is the easiest way to prevent a readied action, having the advantage that it stops all actions that were readied on the same trigger.
In your case, the trigger being "the bard casting his spell" (presumably Faerie Fire), this can be as easy as counterspelling the spell on the turn it is cast using your own reaction, or simply downing the bard before he gets to cast his spell.
Prevent the trigger from being perceived
The reaction is triggered when the character readying an action perceives the declared trigger. As the trigger has to be a perceivable circumstance, this will more than likely rely on the character's senses - so mess with them!
Depending on the trigger, this can be achieved with a multitude of effects and spells, including: grappling and dragging out of range, Chromatic orb, Fog cloud (and other spells that create a heavily obscured area), Blindness/Deafness, Darkness, Silence, illusions, conjuring walls in front of the character, teleporting the character to another plane of existance, etc.
"Convince" the character to ignore the trigger
The character readying the action has to make a choice when the trigger happens. He can take his reaction right after the trigger finishes or ignore it. If you can "convince" him to ignore the trigger, you're safe.
Peaceful ways of achieving this is talking your way out of the situation (which might be relegated to a skill check, but not recommended against PCs). Less than peaceful ways include various mind-altering effects like the following spells: Charm person, Calm emotions (as it makes the character indiferrent about hostile creatures), Suggestion, etc.
Prevent the character from taking the reaction
A character can only take one reaction per round, so denying that can prevent the readied action from happening.
This can be done either by forcing the character to burn his reaction either defensively (using a Shield spell, the Shield master feat, the Sentinel feat, etc) or offensively (for an opportunity attack, battle master maneuver, etc). Additionally, there are some spells that explictly force the character to use its reaction or take it away (be it explicitly or through a condition which does not allow reactions): Dissonate whispers (forces the character to use its reaction to run away), Slow (the target can no longer use reactions), Tasha's hideous laughter (incapacitated), Hold person (paralyzed implies incapacitated), etc.
Additionally, the best condition you can apply to a creature in order to prevent it from taking reactions is dead (or, in case of PCs, unconscious), so downing the character that readied the action could also be a solution.
The case of readied spells
In case of readied spells, you have a few additional options:
note that readied spells require concentration, so simply attacking the caster to attept to break it through a concentration check is enough
Counterspell it on the turn it is cast (using your own reaction)
Dispel it after it has been cast, but before it is triggered - this is because once the spell has been cast as normal, it is no longer an instantaneous spell in the process of being cast, but an ongoing magical effect that requires concentration. Yes, I know, this seems weird and should be house ruled at your table, but it's RAW according to the concentration rules (PHB p. 203) which state that spells that require concentration are not instantaneous - which is a requirement for Counterspell, and the official rules answers for March 2016:
Whenever you wonder whether a spell’s effects can be dispelled or suspended, you need to answer one question: is the spell’s duration instantaneous? If the answer is yes, there is nothing to dispel or suspend. Here’s why: the effects of an instantaneous spell are brought into being by magic, but the effects aren’t sustained by magic (see PH, 203).
Additionally, keep in my that according to this weird tweet delivering the word of God (to be read: Jeremy Crawford), Dispel magic does not require you to see the target:
Jeremy Crawford @JeremyECrawford
@ScottManwell A spell says if its target must be visible. Magic missile's target must be visible, whereas dispel magic's needn't be.