What is the Importance of Acid Alcohol and Sodium Bicarbonate during staining?
This is described with better detail (and better prose) in John Baker's classic description at StainsFile, but to summarize:  The procedure you're describing is a regressive hematoxylin stain with Harris hematoxylin.  To start off with, let's bear in mind that hematoxylin, a compound from the wood of the logwood tree, is actually used as hematein, by oxidizing it with sodium iodate.  (The colorless hematoxylin would naturally &quot;ripen&quot;, oxidize over 4-10 weeks in the presence of air, even without that step, but this is more controllable)  Additionally, aluminum ions are added as a mordant, creating hemalum by binding =O and -OH on the hematein.  The Al atom is what actually binds to something in the nucleus (I found reference to lysine side chains of histone proteins and the phosphate of the DNA - I haven't sorted this part out yet).
When acid is added, it competes with aluminum, which can be thought of as Al3+.  The real bonding may be more covalent than that, but that point is considered controversial.  For whatever reasons, the H+ interferes with the Al3+ mediated attachment of stain to tissue, especially at sites of background attachment (differentiation).  The hematoxylin washes away somewhat, leaving lighter, more specific staining.  (this tactic is called a regressive stain, and is certainly not needed to do the procedure.  This is very much more art than science at this point...)
But ... the acidic hematoxylin has a reddish color, and it isn't as blue as it can be unless it is neutralized to around pH 8 - hence the second step with bicarbonate, though often plain tap water can be used.  That is an ordinary instance of a dye changing color with pH, and can be called &quot;bluing the hematoxylin&quot;.