Without a macro, the only way is to open the Insert > Bookmark dialog,
highlight one bookmark at a time and click Delete, and repeat until
they're all gone.
What's your objection to a macro? Especially one as simple as
Sub DeleteAllBookmarks()
Dim i As Integer
For i = 1 To ActiveDocument.Bookmarks.Count
ActiveDocument.Bookmarks(1).Delete
Next i
End Sub