Can bailiffs take money from a bank account?

No

Bailiffs are only authorised to take control of the debtors goods.^[1]

Some creditors may apply to the court for a Third party debt order,^[2][3] but this is done by a solicitor.

Third party debt orders do not apply to unpaid council tax, magistrates court fines and traffic contravention debts.

^{[1] Paragraph 10 of Schedule 12 of the Tribunals Courts and Enforcement Act 2007
[2] Part 72.2 of the Civil Procedure Rules
[3] Practice Direction 72 – Third Party Debt Orders}