Thank you for your response.
A reason for the issue is that the files which are included to a bundle are absent locally.
TWS doesn't require to create all of the members inside a bundle, however, in the case when members are present in a bundle in your organization, the IDE needs to have them locally in your TWS project.
This is a currently implemented mechanism: when you open any bundle in the editor, the IDE opens all included members and all of the other processes, like pull or deploy, are based on the work on a whole bundle. And the information about a bundle and its members is included in a project file.
Also, I should note, that we consider changes for Lightning functionality, and probably in the future, we will implement a mechanism when you are able to work on each Lightning file separately. However, currently there are some dependencies between a bundle and its members and this is a core for the work on Lightning in the IDE.
We are looking for the best way to provide you with all the necessary and additionally useful features for the Lightning, and I will keep you updated on our progress on this. I believe we will start working on such changes during the nearest months.