Sharing your bank account number is safe and that's how people get money such as their payroll checks deposited directly into their bank accounts from their employees.
You signup to have your paycheck sent to you by direct deposit the employer will need your bank account number as well as routing number.
No one will be able to pull money out of your bank account with those details.
They'll need a lot more information to take money from your bank account so sharing your bank account number is safe.
Bank account numbers as well as your routing number are also on checks you write so they're not secret anyway.