Can a bailiff enter my children's bedroom?

No

Bailiffs cannot enforce writs or warrants by taking control of goods against any debtor who is a child.^[1]

A child is a person under the age of 16.^[2]

Bailiffs do not have a power to search anyone's property to satisfy themselves the debtor does not live there.^[3]

In reality, bailiffs may threaten to enter a child's bedroom to coerce the parent to give a money transfer to get relief from the threat.

If a bailiff gets inside your home, even if the entry is legitimate, record everything on video, and call the police reporting a disturbance. You will be treated with a lot more respect while you are recording everything, because it can be used at court.^[3]

^{[1] Regulation 10 of the Taking Control of Goods Regulations 2013
[2] Regulation 2 of the Taking Control of Goods Regulations 2013
[3] See Neil Tunstall vs Direct Collections Bailiffs Limited (DCBL) and Mr Hussain}