You think that stops my theory?
The culprit was Meridith! She lured Betty into the library and killed her from the hidden passage, with a gun. Meridith never entered the room. The purpose of convincing Betty to lock the door was to create an illusion of a closed room. Meridith wanted to kill Betty out of spite of Betty’s promiscuity in the past.
Alternatively,
The culprit was Meridith! She lured Betty into the library and killed her, with a gun (perhaps given to her by Mr.Ward) after Mr. Wad opened the door. Mr.Ward, being Meridith’s accomplice, then notified the police. Meridith escaped the room using a hidden passage. The purpose of locking the door was to create an illusion of a closed room. Meridith wanted to kill Betty out of spite of Betty’s promiscuity in the past. Ward became Meridith’s accomplice either through bribery, a personal vendetta against Betty herself (perhaps Betty was his lover in the past), or Meridith/Ward were in a relationship themselves.