Permit me to first focus on the example you give in a comment you left: Taken from an email update from a business, Gouletpens.com, with whom I do business: "What is your favorite part of helping out with vacation bible school?" The question was part of a Q & A article which featured an interview with an employee of Goulet Pens. The Goulets (Brian and Rachel) make no bones about being Christians, so the appearance of the word "bible" without capitalization kind of took me by surprise. (BTW, the word "Bible" is capitalized elsewhere in the newsletter.)
For a Christian to write “vacation bible school” in one place and then to capitalise Bible elsewhere suggests either a typographical error or a lapse in concentration. That can happen. Nevertheless, I have also observed an increase in the times I’ve seen Bible written as bible. I have no statistics or facts to support that this is a definite trend, but it is possible that some younger people are perhaps ignorant of the reason why writing “bible” can suggest a lack of respect. Here is a partial quote from an article that helps to explain the history behind the word bible:
The word bible simply means “book.” The English word bible is ultimately derived from the Greek term biblia, meaning “books.” Biblia is the plural form of biblion, which denotes any written document, but originally one inscribed on papyrus. Our word Bible eventually came to be used for the collection of 66 Old and New Testament books recognized by Christians as the canon of Scripture.
The Greek phrase ta biblia to hagia meant “the holy books.” The first Christian use of the term ta biblia, or “the books,” to designate the Holy Scriptures is believed to be in 2 Clement 2:14, written around AD 150: “The books and the apostles plainly declare that the Church hath been from the beginning.” In Latin, the Greek phrase became biblia sacra. In Old French, the word biblia became bible. Old English already had a word for the Scriptures, biblioðece, taken from the Latin word for “library.” But the shorter Old French word bible replaced it in the early fourteenth century....
Capitalized, Bible usually refers to the Holy Scriptures as understood by Christians around the world. More information here: https://www.gotquestions.org/what-does-word-Bible-mean.html
I suspect that people of our generation were brought up to show respect for the Word of God by capitalising ‘Bible’ to indicate we were speaking about the Holy Bible. Certainly the historian Melvyn Bragg ensured ‘Bible’ was always capitalised when he wrote about the history of the King James Bible between its publication in 1611 and its impact on civilisation 400 years later in 2011. The best book I’ve read in the last ten years. 
Alas, with the advent of texting on mobile phones and the questionable punctuation, grammar and sentence structures finding their way into daily newspapers , let alone school rooms, this tendency to write ‘bible’ where it should be capitalised appears to be gaining momentum.
I agree with you that I am also “somewhat concerned... that the use of the word bible, when referring to the Holy Bible, may be related to a general devaluing of this traditionally sacred book.”
 The Book of Books – the radical impact of the King James Bible 1611 – 2011 by Melvyn Bragg, published 2011 by Hodder & Stoughton ISBN 978-1-444-70515-7
 Each sentence is now a paragraph. A single space appears between the last word and a question mark or between the last word and a colon or semi-colon. Nobody gives two spaces between sentences except, perhaps, those of us who were professional typists way back when such things were the standard.
P.S. The best book I’ve read in the last year is The Revelation of Jesus Christ by John Metcalfe (The Publishing Trust 1998 ISBN 1 870039 77 7) – published 1998 but now only available through Amazon.