It is not clear when or how the nice – always appropriate and never required – the custom of beginning a letter with B” H or BS” D – or to be more precise their Hebrew equivalents ב״ה or בס״ד, started. There are those who point to Rabbi Yehuda HaChassid (Rabbi Judah the Pious, 1150-1217) and his work Sefer Chassidim as a possible source for the custom of mentioning G-d before writing an ordinary letter. It seems that Christopher Columbus (Genoa, 1451 – Valladolid, May 20, 1506, one of the most famous explorers of the Age of Discoveries) in almost all of his letters to his son, included at the top left-hand corner what appears to be the Hebrew letters ב “ה 
B” H (ב״ה) is an abbreviation for the Hebrew words baruch Hashem (“blessed is G‑d”) or b’ezrat Hashem (“with the help of G‑d”).
BS” D (בס״ד) is an abbreviation for the Aramaic phrase b’syata d’shmaya (“with the help of heaven”).
T.G. is an abbreviation for the English phrase “Thank G-d.”
“By the Grace of G-d” can also be used.
The choice between B “H and BS “D is personal. There are those who prefer to use BS “D because the “H” stands for G-ds Name, one does not want to use it in letters that can be discarded. This is because one should not disrespect or erase G-d’s Name. Others are using B” H because it is said to be of an older tradition. The Lubavitscher Rebbe encourages to use of B “H, because “H” does not stand for an actual name but for Hashem.1
The question arises whether it is also a good idea for Noahides to adopt this custom if they wish.
There will come a day when the whole world recognizes that “G-d is One and His Name is One,”  Starting a letter in this manner is a way through which there arises more awareness among people that there is a G-d who sees and hears and is Omnipresent.
It is an excellent habit to contemplate G-d, especially for the normal things in life. Therefore, it is also a good custom for Noahides to begin a letter or writing in this way and to help to develop the awareness of G-d around the world. It is wise since many non-Jewish people do not know Hebrew or know about the abbreviation – to use one of the English variants.
There is strictly no need to use these abbreviations with a blog or email or any other electronic means. However, since there is a chance that people will print it out, which does make it a text written on paper, one may choose to do the same with electronic writing.
In addition to the custom of beginning written in this way, it is a good custom to mention G-d even during conversations with people. This custom already had the ancestor in a Midrash points about Jacob when he pretended to be his unruly brother as a ruse to get his father, Isaac, to bless him, he almost betrayed himself, Jacob by repeatedly mentioning G-d in his conversation with his blind father.1
You may find that if you are speaking with an observant Jew and you ask her how she’s doing, she’ll preface her answer with the words, “Thank God” or perhaps the Hebrew, “Baruch Hashem.” This is a similar concept, making sure to credit G-d or thank G-d for the ability to answer a question as simple as “How are you?”
Let us make it a habit to thank G-d in our conversations and writing for both the good He gives us, and the good we experience as covered.
By Angelique Sijbolts
 Why Write B”H or BS”D at Head of a Letter, and What Does It Mean?
 AskNoah Q&A Forum
 Rabbi Yosef Rosen, the Rogatchover
 See the paragraph “What to Do with Written Holy Names?” In the blog Deutronomy 7:5 – Should we destroy idols, and what about idolatrous books?
 Harerei Kedem B 124 Rav Solovaichik
 Zechariah 14:9.
 Ask the Expert: Why do Some People Write Three Hebrew Letters On Their Notes?