The website of Library of Congress provides us with a following description regarding the overall problem with uniforms during the First Battle of Bull Run:
As Union and Confederate troops met for the first great land battle of
the war, confusion was the only constant. Lack of standardized
uniforms made it difficult to tell friend from foe.
Still, particular army units had their own uniform standards. Some of the nicknames of those units come from the clothes, f.e. Red-legged Devils, which points to the red trousers of 14th New York State Militia uniforms.
There's a website http://www.firstbullrun.co.uk, which is dedicated to soldiers of this particular battle. You will find there a lot of interesting informations about uniforms worn during the battle by particular military units. It provides excellent choice of quotes from valuable sources, which in many situations talk about the uniforms. Everything is divided according to a division, brigade and particular unit.
Also the website contains paintings of each unit, that were done with full respect to those researches.
Here's an example, for 2nd Maine Infantry (1st Brigade, 1st Division of Northeastern Virginia army):
"After going a short distance, he saw ahead of him in the woods some
men wearing a grey uniform (quite a number of our northern regiments
at the time wore a grey uniform very similar to that worn by the
rebels, the Second Maine among the rest)."
"The uniforms were grey throughout with drab felt hats, regulation
The website is full of such descriptions for various units, so you'll find what you're looking for depending on what's the exact aim of the research.
Also be sure to check their reference materials, there are some good books recommendations for you.