As an example of what can go wrong, look at UN Security Council Resolution 242, which passed in 1967. I am deliberately not going to go down the rabbit hole just for the sake of giving an example of what your question was asking. I am going to request that people please not use this answer to argue about the larger conflict this is a facet of or explain to everyone which side is obviously wrong.
The English version calls for the withdrawal of forces “from territories occupied in the recent conflict.” The French version calls for something different: withdrawal “des territoires occupés”, or literally, “from the territories occupied.” That’s what started more than fifty years of arguments.
Some lawyers have argued that the English version should take priority and means withdrawal from only some of the territories was acceptable. Others give arguments that the French version is equally valid or a correct translation that tells us how to interpret the ambiguity in English. The American Secretary of State, Dean Rusk, who helped negotiate the text, writes in his memoirs that it was intentionally left vague as a compromise:
There was much bickering over whether that resolution should say from "the" territories or from "all" territories. In the French version, which is equally authentic, it says withdrawal de territory, with de meaning "the." We wanted that to be left a little vague and subject to future negotiation [....]
A diplomatic resolution can “be left a little vague” because there is no way to enforce it, neither side believes the dispute should be resolved by lawyers arguing over what it means when there is or isn’t a definite article in the literal text of a United Nations resolution anyway, and all that’s ever really been at stake in this particular argument is point-scoring in speeches. (Yet, at the same time, it’s related to a very important topic that people are extremely motivated to argue about.)
But be careful if your legal contract ends up being negotiated like a diplomatic compromise. If you are interested in looking up the details of this dispute, here is the Wikipedia page. And here is the equally-authentic French version.
There was a good comment pointing out an important difference between your situation and this one: you’re contemplating that both sides can at least agree on which legal process will resolve any dispute and render a decision. This is very true.
I think, though, that this still shows how fundamentally impossible it is to decide what a text really means when there are two equally-authoritative versions of it that say different things. And you do not have even a hope of catching every possible ambiguity and discrepancy between English and Bulgarian, even if removing all of them were possible. The whole reason you don’t want to go by the Bulgarian contract is that you don’t trust your side’s understanding of what it says. If you believed you knew Bulgarian well enough to make this idea work, you wouldn’t need to.