TL;DR - It is the kata that is derived from the bunkai, not the bunkai that are derived from the kata. In fact, kata are mnemonic tools intended for advanced students to remember the bunkai and eventually transmit the art. If you do not know the bunkai for your kata, the best way to reconstruct them would be to cross-train in jujutsu, judo or other stand-up grappling art.
To properly answer this question, one must first ask "what are kata?"
One "popular" opinion would have you believe that kata are nothing more than choreographic exercises meant to keep students involved in the classes prior to the now mainstream belt system (thanks, Judo!). While I agree with the expressed sentiment that modern martial arts classes are too focused on forms and kata rather than on practical application, this opinion is very limited. In Okinawan karate, at least, kata are so much more than just a lazy teaching gimmick.
Individual schools did not teach dozens of kata
Okinawan karate used to be a somewhat "secret" thing. Meant as a complement to folk wrestling (mutou or tegumi, depending on the region), it was mostly a family affair in how it spread and evolved. A master would go on to teach to his sons, and perhaps to those of close friends that were unfit to teach for various reasons (such as never mastering their own father's style before he died). While people would fight and train with each other, the original kata didn't spread much outside of their local circles.
Each of these family schools had maybe one to three katas, and they contained most of what made the style "unique". These kata were jealously guarded, only taught to loyal students and trusted friends. With time, however, karate became less popular and the number of qualified masters dropped. To further develop their art, students eventually had to study with various masters, learning their respective kata. This is why modern styles such as Shotokan and Kyokushin teach so many kata. More doesn't necessarily equates to better, however, as the advanced techniques contained within were often diluted as each kata was practiced less and less (because more katas).
Kata are mnemonic tools
Historically speaking, basic karate techniques are very similar from one style to another. Considering the human body is built in a specific way, the number of possible punches and kicks is somewhat limited, which in turn influences the number of effective blocking techniques. However, one needs to consider the fact that early karateka pretty much all cross-trained in wrestling arts. Individual styles thus emerged by focusing on how to switch from striking to grappling, or how to use grappling to gain an advantageous position to strike from.
How do you teach these transitions? Continuously practicing them seems like a decent solution. But when all of your reputation is built on the strength of your style, how do you ensure that it gets fully transmitted to your martial heirs? You could write it down, of course, but then you'd risk it being copied and/or stolen. This is where kata truly shine.
Kata are built upon layers. The first layer is what you see: a combination of punches, kicks, and blocks. This layer is intended for beginners, where they can practice their basics using an exaggerated stance (to develop muscle and muscle memory for maximum efficiency) before moving on to sparring where the stance is much more relaxed.
The second layer is what most people would nowadays call "kihon". Using the first layer's techniques, you now train them outside of the kata in short combinations (like gedan barai followed by a gyaku tsuki counter), usually with a partner. Again, the kata serves as a practice tool to develop muscle memory, but it now becomes a greater teaching tool, in that in gives a structure to the techniques and organizes them in short sequences.
The third layer is intended for more advanced students. Once one truly understands the fundamentals, as well as having a decent understanding of grappling, the order in which the techniques are presented in the kata indicate transition points where grappling is involved. What initially looked like a uchi ude uke followed by a step forward and punch now becomes a leg grab followed by a takedown, with both push and sweep variations (represented by the punch and the forward step, respectively).
At this point, having practiced kata for years, students are unlikely to forget them. This is what makes kata such interesting teaching tools: by the time the students truly master the techniques within, they have already practiced the kata so many times that they will never forget it, meaning that the style should never be "lost". Sadly, that's not what happened...
I guess my point here is that kata are much more than a collection of basic techniques. They are instructions, or perhaps blueprints, on how to reconstruct the more advanced techniques of the style.
How do you create bunkai for a specific kata?
To put it bluntly, you don't. Kata were not created according to some fleeting whim; they were carefully crafted in order to maximize the training benefits for students as they progressed in their mastery of the style. In fact, the bunkai came before the kata.
As the masters' styles evolved, they drilled their students on the techniques that were deemed most effective at the time. These drills eventually became the core of their kata, which was to be used by later generations of masters to remember the original drills. But these drills could not be too obvious, otherwise anybody watching you perform a kata could instantly decode your prized techniques, so they were "approximated" using basic punches, kicks, and blocks. That way, only someone trained in your style, or someone that had a profound understanding of both karate and wrestling, could make use of it.
Sadly, as martial arts in general became less and less popular, much of the hidden meaning of these kata was forgotten. Instead of figuring out all of the knowledge in their own style's kata, many practitioners traveled and learned other styles' kata to complement their training. Indeed, as different styles focus on different techniques, their respective kata will have different more "obvious" bunkai. Quantity is now used as a substitute for quality when it comes to kata and, from my experience, around 75% of the bunkai for each kata that were taught to me were recent fabrication because the original meaning was long lost.
What can I do, then, if I wasn't taught the original bunkai for my kata?
My best suggestion to you would be to learn classical jujutsu, judo, or other Japanese grappling art that have a good stand-up game, and try to reconstruct the bunkai that were lost. While your reverse-engineering might not look at all like the original creator of the kata intended it, it will likely be closer to his original intent than simply practicing combinations of kicks and punches.