Once after adding the components to the package how can we remove fields or classes that are not needed as a bulk instead of removing one by one?
Bear in mind that if it's a managed package, some of your components may be locked in. Not sure what you mean to remove them 'in bulk', as you surely need to handpick what to remove.
I would download all the metadata using the Force.com migration tool, edit the local metadata files to remove what you want removed, then upload everything again using the same tool. That can be quicker than removing things by point-and-click in the UI.
Does that count as 'bulk removal' for you?
You have a few options. My recommendation however, will be to use ANT and destructiveChanges.xml contrary to your post. It might take a few hours to set ANT up in your environment and in your support team's environment, but it is a repeatable process you can run on multiple orgs if need-be.
Running the ANT script (can) be easier for your support team rather than manually deleting the classes and triggers or installing eclipse on their local machines and deleting the files that way.
If you really want to get crazy with it, and simplify it for your support team, you could even set up a CI tool that would allow a push button delete of the classes, which would fire the ant migration toolkit script to delete the files from a designated org.
More info on the destructiveChanges approach is here: http://wiki.developerforce.com/page/Propagating_Destructive_Changes
While the previous answers does answer your question I do have an addition to the answers ( I can't comment yet due to low reputation ).
What i'm not getting from your post is if the "package" is a managed or unmanaged package.
In managed packages you're not allowed to remove any components from your package once it's been released. There is pilot running you can apply to by raising a case.
More information on the pilot can be found here: http://releasenotes.docs.salesforce.com/en-us/winter14/release-notes/rn_186_isvforce_managed_component_deletion.htm