What is the ruling on depositing a trust amount into a private business bank account out of fear for it?

You are not permitted to spend the money deposited with you, because it is a trust (wadi'ah). It is obligatory to safeguard it and return it to its owner, based on the Almighty's saying: ﴿Indeed, Allah commands you to render trusts to whom they are due﴾ [An-Nisa: 58], and the Prophet, peace and blessings be upon him, said: «Render the trust to the one who entrusted you, and do not betray the one who betrayed you.» As for placing the money in your bank account without the owner's permission, this might obligate you to guarantee it, due to the mixing of the two funds and their indistinguishability. Therefore, you must inform the owner of the money; if he agrees, then all is well; otherwise, you must return his money to him.