This can simply be done by adding this field to a Form in an Asset Table.
Go to Forms > View Form Templates > Select the form you want to add this to > Form Builder tab > From the CRM drop down you can drag and drop Asset Item or Asset List > Modify Single Asset or Asset List > Select Asset Type as None > Refresh the page and choose they type again for the new fields to be visible.
To add the extra entry fields to the form itself drag and drop a Text Field inside of the table / list. Then select Asset List or Asset Item again, and in the list of Asset fields, select the object name for the new field you just added in the drop down for the Asset field you want to display.