Who can link the #IR to the bill? How do you link this to the bill?

Custom field (list/record, sourcing from transaction, filtered to IR) would allow you to select the IR# but not sure of you could have this automatically populated as I don't think there's a direct linkage.

why doesnt the IR # show up on the bill? is this because of the PO?

You aren't creating the Bill from the IR so there isn't a link. You could also potentially have multiple IR related to a single PO which is then billed as a single Bill.

But I am creating a bill from the PO

Aye, from the PO and not from the IR. If some have an "associated" IR then my suggestion is as above, create a custom field, type of list/record sourcing from transaction, filter to type = IR and IR.createdfrom is equal to Bill.createdfrom. You can then select the appropriate IR on the Bill form.