The family members think Jesus is pretty cool, and decide to become Christians too. Then, the wife baptizes herself, and the wife baptizes the son and daughter. Then, Bob and his family start a close-knit family "church"... with only 4 church attendants.
It's great that Bob and his family are doing whatever they can to bring God into their household and lives. They are not waiting for everything to be perfect, or for others to approve of their faith, or adding a year's delay before they get comfortable in a church. They are moving forward, and if a mistake was made, then it can be corrected later.
Maybe when their church grows, everyone can have a more public ceremony -- have an event at a lake, with friends and family invited. If they end up at a church, most pastors will gladly perform a public ceremony to make it feel more official.
JESUS
Imagine how many followers Jesus had the 30 years before His public ministry. His mom, his aunt...probably His cousin John... Jesus adhered to Judaism, but started Christianity with a handful of believers.
His baptism was public and administered by others, but His favor with His Father did not start at that moment.
Jesus taught empowerment of believers, how one child can bring a loaf and fish, and God can multiply it out to feed thousands. It is not about what we do, but what we allow God to do through us.
ABRAM
Look at the early chapters on Abraham--God sent him outward to claim land. He had to enter a land with no synagogues, no believers... and carry on His faith in God.
Genesis 12:
The LORD had said to Abram, "Leave your country, your people and your father's household and go to the land I will show you.
"I will make you into a great nation
and I will bless you;
I will make your name great,
and you will be a blessing.
I will bless those who bless you,
and whoever curses you I will curse;
and all peoples on earth
will be blessed through you."
So Abram left, as the LORD had told him; and Lot went with him... He took his wife Sarai, his nephew Lot, all the possessions they had accumulated and the people they had acquired in Haran, and they set out for the land of Canaan.
In Genesis 15:
"I am the LORD, who brought you out of Ur of the Chaldeans to give you this land to take possession of it."
On that day the LORD made a covenant with Abram and said, "To your descendants I give this land, from the river of Egypt to the great river, the Euphrates- the land of the Kenites, Kenizzites, Kadmonites, Hittites, Perizzites, Rephaites, Amorites, Canaanites, Girgashites and Jebusites."
These were not religious-tolerant nations.
JOSEPH
Fancy-coat Joseph left his homeland and had to carry on his faith when he knew no other Jews. He honored the Jewish faith by inviting G-d to do mighty things through him in Egypt. He brought Judaism into the home of the man considered a sun god, all by himself.
Some people do not have the luxury of churches on every corner.
TODAY
Some people here on the forum live in Islamic or Communist nations, where their lives and families would be endangered in public Christian ceremonies.
If churches and fellowships are available, then independent baptism is a little lonely, don't you think?
There is evidence that the Jews of Jesus' day already practiced baptism, with a different premise than we do today. If you have time, read about the Mikveh ceremony.
http://jewishencyclopedia.com/articles/2456-baptism
"According to rabbinical teachings, which dominated even during the existence of the Temple (Pes. viii. 8), Baptism, next to circumcision and sacrifice, was an absolutely necessary condition to be fulfilled by a proselyte to Judaism (Yeb. 46
b, 47
b; Ker. 9
a; 'Ab. Zarah 57
a; Shab. 135
a; Yer. Kid. iii. 14, 64
d)."
Ezek. xxxvi. 25, "Then will I sprinkle clean water upon you, and ye shall be clean."