Here are some tips to streamline your workflow. In addition to this, you may need to consider creating additional scripts.
Firstly, I recommend saving the podspec file to the root of your project. So, DependencyB.git will have a DependencyB.podspec file.
Simplify step 3
Change the source tag for the version link. Thus, you only need to change the version string in your podspec.
s.source = { :git => "https://github.com/Organization/DependencyB.git", :tag => "#{s.version}" }
Simplify steps 5, 6 and 7
Run the following from the DependencyB.git directory. (Assuming you have your podspec there, as I suggested above)
pod push OrganizationPrivateRepo DependencyB.podspec
If DependencyB.podspec is the only podspec file, you don't even need to include it in the line, giving way:
pod push OrganizationPrivateRepo
Step 4
Finally, I think simplification of step 4 is possible, but this is one of those things that varies between organizations and individual developers, as it is part of their workflow. For example, I usually pass in an IDE from my environment.
Such scripts can be integrated into podspec to update the s.version value. Or, alternatively, get the correct tag from the s.version value.
UPDATE: Simplify Step 2
It looks like you are making changes to DependencyB twice. You can customize CocoaPods symbolic link. In the Projectfile Podfile, specify the following:
pod 'DependencyB', :path => "../path/to/DependencyB'
Now you can edit files in DependencyB from ProjectA. After making this change, you will need to run pod update . After this, changes to the source will be available immediately, as this is a symbolic link. I am having trouble running Git commits from Xcode while doing this, but other than that it works well.