How do you access the Custom Field Label captions for a vendor? Not the data in the Custom Fields, but the actual Custom Field Label name?

Custom Fields are created within QuickBooks. The Label names can also be modified at any time also. In your example, when editing a Vendor, click on the Additional Info tabpage: 

Click on the [   Define Fields   ]  button and create and modify your Custom Fields as required:

In QODBC the Custom Field Label appears as: CustomFieldname (with the name of the custom field, without spaces, as shown in QuickBooks) as can be seen in VB Demo by running:

sp_columns Vendor

To determine the Custom Field names via programming, just do: 

Const adUseClient = 3
rs.CursorLocation = adUseClient

strSQL = "sp_tables"
'Open rs
rs.Open strSQL, cnConnection, adOpenStatic, adLockReadOnly

And loop through the recordset for each table:

then:

strSQL = "sp_Columns """ & sTableName & """"
'Open rs
rs.Open strSQL, cnConnection, adOpenStatic, adLockReadOnly

And spin through the columns for that table.