The prospects for a definitive answer are bleak, because the qualifications for distinct established writing system are not entirely clear. Re: consensus on correctness, if taken literally this is an impossible requirement to actually satisfy. Suppose that "American English" is a language with an established writing system, is different from the British English writing system (see well-known spelling differences like theater, color, the suffix -ize). There is no way to determine the consensus spelling of accommodate, reference, until. There aren't any practical but scientifically valid survey methods that would tell you what most people think is the correct spelling. Psychology tests will sample only current undergraduates in universities enrolled in courses where they are compelled to be experimental subjects, which is not a valid basis for extrapolating to the population (which anyhow first needs to be defined, since 7 year olds do not have valid opinions). Sampling from written samples likewise gives you a highly skewed sample. There are normative answers contained in pedagogical spelling materials and dictionaries, but appeal to authority is quite anti-consensus. I'm not arguing for a populist approach to spelling, I'm arguing that the issue of standards needs to be sharpened up. I would say that there is a standard for American English spelling (so, yes, I am arguing for appeal to authoritative sources), but it is not rigorously respected, to the point that "nite" is not generally considered a misspelling anymore. Question: do you could "nite, brite, lite" spelling as defining a distinct writing system, or not?
Within the sphere of American English, you would almost certainly have to recognize a number of dialect variants. Some people pronounce "thing" as [θæŋ], and some people pronounce "with" as [wɪf]. While we don't find large-scale adaptation of "thang" and "wif" in writing, a number of authors writing (partially or wholely) in those dialects do employ alternative dialect spellings. Should we recognise this as a different standard (insofar as it is reasonably standard within the context of writing those dialects)?
The desideratum that "There should be a relevant number of native speakers that used it and traded it to their children" seems reasonable, since probably all languages with at least a dozen speakers have some written materials created by a linguist, but there hasn't been uptake on all of those efforts. The idea that native speaker parents teach their children how to write is maybe a bit over-optimistic (I learned how to write in school, my parents didn't teach me, and actually one of my teachers was not a native speaker though she know how to read, write and teach English). If we substitute the desideratum "is adopted by native speakers", and stipulate that the system should be used by at least one person not professionally engaged in promulgating the writing system, then we may have a suitable filter. If you want a larger set of professionally-disinterested writers (e.g. "at least 100 individuals"), this would filter out very many languages, over 10% of current languages, which have too few speakers, and probably much more than that because minor languages tend to have literacy problems.
In languages whose writing systems are newly developed, especially in African languages, the phonemic system is rich and the orthography often includes many distinctions that are unattractive to speakers – symbols like ɪ ʊ ə ʃ š ŋ plus diacritics as in á à ̋a ǎ. There is an observed tendency to omit such diacritics, which would lead to distinct writing systems (the officially sanctioned system, versus the system used by people). Hence official Kikuyu distinguishes [i ĩ u ũ] and ordinary writing omits the diacritic -- does this count as two writing systems?
Depending on how these issues are resolved, the ballpark would be on the order of 10,000 systems.
The reason for the up-tick relative to the number of Ethnologue-listed languages is because of the aforementioned factors. For instance, Lule Saami has different writing systems for Norway and Sweden but it's one language. Surprisingly, English is a single language (but multiple writing systems). I'm also including increases for historical changes in spelling. North Saami has had at least 4 spelling systems over about 400 years; languages spoken in the Russian sphere of influence (esp. the southern zone) have changed between Cyrillic, Latin, Arabic and other bases for writing within the past 150 years; many African languages have gone through two or three spelling systems just within 100 years. There are also quite a number of writing systems in India, for instance Punjabi which has two (Indian and Pakistani), Devanagari, Bengali, Gujarati, Tamil, Telugu, Malayalam, Kannada... Each of these has a distinct script.
The statement "different languages, if written, do usually define different writing systems (like English and Spanish)" is a bit unclear. English does not use <ñ> or any accents, which Spanish does. Maybe you mean that because of those different letters, English and Spanish have different writing systems. Shona and Swahili are completely different languages, but they happen to use the same letters from the Latin alphabet, so you might say that they have the same writing system (even though there are combinations in one that aren't possible in the other: <sv, tsv, bh, n'> in Shona, <gh, ng'> in Swahili.
If you want to restrict the set of "established writing systems", I would suggest (1) being lax about "sameness" whereby "color" and "colour" don't reflect different writing systems, they reflect different spellings and (2) raise the bar on what it takes to be "established": government recognition might be what you're after.
