(I don't actually know if it's okay to post this for copyright reasons or whatever so please take this down if that is an issue.)
I want to doubt that a DM Screen is anything like an authoritative source, but the D&D 5e Screen (found here courtesy of @Adam in the comments) does have suggestions for Audibility ranges:
Trying to be quiet 2d6 x 5 feet
Normal noise level 2d6 x 10 feet
Very loud 2d6 x 50 feet
The way I read that is that for a given noise, it reaches out to the given distance in feet and after that, well I'm not quite sure. Either it refers to being able to understand a sound (for instance speech) or being able to hear it at all.
In your example, obviously the sounds of battle will be Very loud. Whether that imposes Disadvantage on Perception checks or a penalty to the character's Passive Perception score is debatable, and it can be negated with Advantage anyways. The most important question is whether a Stealth check that is under the Passive Perception score should count as trying to be quiet versus normal noise level.
Obviously by virtue of the Stealth check they are trying to be quiet but on the flip side they were not actually quiet enough. If that is sufficient to call it a Normal noise level then on average (average of 2d6 is 7) the normal hearing range is 70 feet, and there is a very, very good chance the sneak in the bushes will be heard by the blinded character.
Important: (I just noticed) This information is on a table under the heading "Encounter Distance" which may mean that these numbers are not as suitable for your scenario as they are for figuring out when creatures notice each other. Take that as you need to, but it is definitely a starting point.