By "the larger amount of pizza" I think you mean if there's more than half of the pizza left.
Pizza is usually cut into slices before being served. Let's say this particular pizza is cut into eight slices. Person B gives person A two slices. Person A eats them both and says:
I ate all of the pizza you gave me.
Person B then states that there are some more slices:
There are some more slices if you want to eat.
This could be anywhere from two to six slices, so less than half or more than half. Because they said "slices" we know there's more than one slice left (unless person B make a mistake).
Instead of this, person B could say:
There is a bit more pizza.
This implies that there is not much pizza left, at least one slice but probably less than half a pizza.
Note that "some more" could refer either to slices of pizza or just pizza. "a bit more" can only refer to pizza, not to slices because "slice" is a count noun, whereas "pizza" is a mass noun. You can say "a few more slices" if there are not many left.
some more pizza
some more slices
a bit more pizza
a few more slices
I have only considered the case where there is one pizza. If there is more than one pizza, it is almost exactly the same, but "a bit more" pizza might be a greater amount of pizza (more slices) than with only one pizza.
If I haven't fully understood your question, please clarify it and I will update this answer.