「[割愛]{かつあい}」 is a formal word so appropriate to use in a formal situation as suggested by eltonjohnさん.
「[飛]{と}ばす」and 「[省略]{しょうりゃく}する」 have similar meanings, but 「割愛する」 is more appropriate in this case, because 「割愛」 is formal and has a special nuance for it. While 「飛ばす」 and 「省略する」 simply mean "omit", 「割愛する」 means "I do not want to omit [this/it/etc] but now I need to due to the inevitable reason, so I omit [this/it/etc] for this time".
Here are some examples of sentences using 「割愛する」 in a colloquial context in a formal situation.
「[時間]{じかん}の[関係]{かんけい}[上]{じょう}(/[都合]{つごう}[上]{じょう})、[内容]{ないよう}の[一部]{いちぶ}を[割愛]{かつあい}させていただく[場合]{ばあい}がございますが、ご[了承]{りょうしょう}いただければと[思]{おも}います」(If the speaker says this at the beginning, s/he does not have to mention the time matter after that.)
「[続]{つづ}きまして(イ)がございますが、[本日]{ほんじつ}は時間の関係上、[割愛]{かつあい}させていただきます。[次]{つぎ}の2ページに[参]{まい}りまして(ウ)からとなりますが、……」(If the speaker mentions the time matter at the point s/he does the first 割愛, s/he does not have to mention the time matter after that.)
「続きまして、3ページ[目]{め}に[移]{うつ}りまして(エ)がございますが、こちらは割愛させていただきまして、(オ)に参ります」
「[次]{つぎ}の(カ)は割愛させていただきまして、5ページ目の(キ)に参ります」
「(ク)は割愛いたします。次の(ケ)でございますが、……」
「(コ)は割愛いたしまして、(サ)に参ります」
A [敬語]{けいご} form of 「飛ばす」 is 「飛ばさせていただきます」. Here is an example of the usage.
「おめくりいただきまして、[次]{つぎ}の7ページからは(シ)となっておりますが、9ページまで[飛]{と}ばさせていただきまして、(ス)に[参]{まい}りたいと[思]{おも}います」
Each of (イ)〜(ス) above represents the sectional title or a brief account/summary of the part which will be omitted. Because the speaker thinks that the part is still important although s/he omits it this time, s/he does not forget to present what the omitted part is about, especially when using 「割愛」.
However, there are many Japanese people who don't know the original meaning of「割愛する」 and think that the meaning of the word is "omit an unnecessary part". According to 『平成23年度「国語に関する世論調査」の結果について』 published in 文化庁 official website, the percentage of Japanese people who understood the original meaning was 17.6% and 65.1% Japanese people believed the "unnecessary"-version meaning.
Anyway, although people understand the meaning of the word differently, the ways to use the word 「割愛」 are almost same in most cases. It's still a formal word, and people use 「割愛」 in a formal situation. If the speaker uses the word 「割愛」, the listeners would think that the speaker is trying to omit it politely.