There is a lot of missing info here. If the OP's child had given the OP's address at the outset, then the OP would have received communications from the train company, court, etc long before it got to the stage of the bailiffs. Did the OP receive any letters addressed to the child, and if so, what did he do with them?
I am also a bit confused about the hand delivered letters. Does the OP just mean the bailiffs personally posted them through his letter box? The standard procedure when issuing something like this is to ask for the named person. If you are not the named person, you simply say so.
Is the OP sure that his child committed fare evasion? Could it be that someone with the same or similar name has given a false address, and the bailiffs have wrongly traced to the OP's address?
If the OP is certain that his child did it, and then dumped the shit at his doorstep, then my reaction would be to pass it straight back. Give the bailiffs the child's current address, if known, or at least be as helpful as he can in helping the bailiffs locate the child.
The bottom line is that if the OP's child won't sort their mess out, then the OP has got to be proactive in getting the bailiffs off his back. Things like this need to be sorted, they just get steadily worse if not dealt with. Always keep a copy of anything like a bailiff's letter, and your response. Just posting it back "not known at this address" is highly unlikely to make the problem go away. If the OP is obstructive or unhelpful, it will just make it look to the bailiffs as though he is hiding something. He needs to be careful that the debt doesn't get linked to him or his address, which could cause all sorts of problems in the future with anything requiring a credit check.