The audio sounds like мігає. Makes it difficult to get a correct answer in "Type What You Hear" version of this exercise.
I've listened to it like 20 times to try to understand what you're talking about.
On first attempt I clearly heard exactly the same as the sentence reads, but then I tried to kind of "zone out" from the sense of the sentence and focus purely on the sounds, and I got your point - the "б" in бігає is a very quick sound, barely distinguishable and could be easily mistaken with other sounds.
But this is how the native speakers speak, even in very careful speech, so you probably just need to get used to it. Once you're experienced enough, you'll be able to reconstruct words and phrases from such quick sounds, you just need some practice.
Please also note that almost every consonant in Ukrainian has two versions - "soft" and "hard". "б" in бігає is a soft б, б in, say, баран is a hard б - they're similar, but, strictly speaking, those are different sounds.
Please compare. Soft б:
They might sound the same to you, or you might find one of those easier to distinguish than the other, I'm not sure, our ears are way too used to the difference.