The document is locked because you didn't close it with the Document.Close method, so the document is still opened and therefore cannot be opened again.
Also avoid using ActiveDocument the document that was opened is set to doc
Set doc = objWord.Documents.Open("test.docx")
and can therefore be referenced with doc.
Dim objWord As New Word.Application
Dim doc As Word.Document
'Dim bkmk As Word.Bookmark
Set doc = objWord.Documents.Open("test.docx")
doc.variables("bookingRef").Value = Me.txtRef.Text
doc.Fields.Update
doc.Save
doc.Close
Also don't forget to quit your Word application after you are done.
objWord.Quit
Otherwise the instance of Word will be open until you shut down your computer.
The Fields.Update method should update the fields, but it might be unsuccessful because of an error. Check it for errors:
If doc.Fields.Update = 0 Then
MsgBox "Update Successful"
Else
MsgBox "Field " & doc.Fields.Update & " has an error"
End If
What I did (a test according comments below this answer):
(following steps according How to store and retrieve variables in Word documents)
Created a file C:\Temp\test.docx
To use the DocVariable field, follow these steps:
On the Insert menu, click Field.

Run the following code in Excel
Option Explicit
Public Sub Test()
Dim objWord As New Word.Application
On Error GoTo CLOSE_WORD_APP 'error handling to ensure there will not be any orphaned and invisible Word application left
Dim doc As Word.Document
Set doc = objWord.Documents.Open("C:\Temp\test.docx")
doc.Variables("bookingRef").Value = "This is the updated Value: " & Time
doc.Fields.Update
doc.Save
doc.Close
CLOSE_WORD_APP:
objWord.Quit SaveChanges:=False
If Err.Number <> 0 Then
Err.Raise Err.Number, Err.Source, Err.Description, Err.HelpFile, Err.HelpContext
End If
End Sub
Open the Word document C:\Temp\test.docx and see that everything is updated:
