Omitting "there" in a sentence

Can I omit there in the following question:

How much juice is there in the bottle?

When is it possible to omit there in a sentence?

Any references to grammar sources are welcome and expected.

The short answer is, Yes you can omit there from the sentence "How much juice is there in the bottle?" without altering its substantive meaning. Though I haven't been able to find a reference work that addresses a specific example where there appears midway through the sentence, as it does in the OP's example, this is clearly an instance of what (in comments beneath the OP's question) John Lawler calls "there-insertion" and what F.E. terms "existential 'there.'" Other authorities use other terms for the same grammatical phenomenon, as Kenneth Wilson, The Columbia Guide to Standard English (1993) observes:

DUMMY SUBJECTS In sentences such as the following, there and it are variously called expletives, empty subjects, anticipatory subjects, or dummy subjects: There is a high wind tonight. There are several latecomers in the lobby. It's easy to see she's worn out. In speech and Informal writing these dummy subjects are handy entries into sentences whose real subjects you have not yet chosen. And sometimes, even in finished writing, the formulaic beginning can be a welcome, pace-changing inversion.

Jeffrey Kaplan, English Grammar Principles and Facts, second edition (1995) adopts F.E.'s terminology:

The Existential Marker: There

There are two theres in English. One expresses location, often as a pro-word for a locative prepositional phrase, as in Don't go near the woods; I told you never to go there!

Another there, the existential one, expresses the existence of something: There is a Santa Claus; There ought to be a traffic light on the corner; In 1492 there was a widespread belief that the earth was flat. In traditional grammar, this there is sometimes called an (or the) "expletive."

R. W. Pence & D. W. Emery, A Grammar of Present-Day English, second edition (1963) offers this analysis [internal citations omitted]:

"THERE" AS AN EXPLETIVE

a. With a finite verb. Like the it-expletive, the there-expletive may serve a valuable rhetorical purpose: it permits placing a subject after its verb without any confusion in meaning. It may serve to mark time until the true subject of the verb appears. The verb be used in conjunction with there is a notional verb. It usually functions as a complete verb; that is, it is used as a verb of complete predication, in the sense of exist and so has no subjective complement. Variations of the there expletive sentence pattern make use of such verbs as seem, appear, happen plus the infinitive to be.

There is always one right way to to do a thing. [The sentence for analysis reads 'One right way to do a thing always is' (is = "exists"). Thus way is the true grammatical subject of is; there, being grammatically (but not rhetorically) superfluous, is an expletive.]

Transforming Pence & Emery's example sentence into a question, we get "How many right ways are there [always] to do a thing?"—which clearly possesses same basic pattern as the OP's "How much juice is there in the bottle?" We might conclude that the rhetorical rationale for there in questions of this form is that they appear in anticipation of an answer of the form "There is [or are] ..."

Nevertheless, the substantive content of "How much juice is there in the bottle?" is no greater than the substantive content of "How much juice is in the bottle?"—and the same is true of the answer "There is a pint of juice in the bottle" versus the answer "A pint of juice is in the bottle."