Does the game send you to do Bonus Series specifically? We now have Nar-Shaddaa and Tatooine BS available, but no prompts to go and play through them. Will it break the story if it's cleaned up before Alderaan?
Thank you and apologies for a noobish question!
The Bonus Series for Nar Shaddaa are supposed to be completed AFTER you complete the first chapter. The ones on Tatooine are to be done when you're still in the planet, as in, BEFORE you leave after you're done with your class story.
If you do the Bonus Series on Nar Shaddaa before going to Alderaan, your character may get overleveled for the latter. Wisest course of action is the one I recommended IMHO.