Quote 1
BOTTOM
An I may hide my face, let me play Thisbe too, I'll
speak in a monstrous little voice. 'Thisne,
Thisne!' 'Ah, Pyramus, lover dear! thy Thisbe dear,
and lady dear!' (1.2.49-52)
When Bottom volunteers to play the role of Thisbe and make his voice high-pitched, Shakespeare alludes to the fact that all female roles were played by male actors on Shakespeare's stage. Usually, these parts were given to boys with high-pitched or "monstrous little" voices.
Quote 2
BOTTOM
I see their knavery. This is to make an ass of
me, to fright me, if they could. (3.1.122-123)
Of course, when Bottom accuses his friends of trying to "make an ass" of him, it's funny to us because we know something that Bottom doesn't—he literally has been made into an ass. (Also, his name, Bottom, becomes very fitting.)