Hi Sven,
Sorry for the inconvenience and hardship.
We have sent you an email[#3937768 dated June 07 2017] with a workaround for the problem "Assign to site in bulk - asset components".
Hope that would help you till the problem is fixed by providing bulk assign for asset components. This change has been taken up by the development team on high priority.
We shall keep you informed on the updates on its release/availability.
Please do get back to us for any further details or queries.
Thanks & Regards,
Saravana Balaji .S
ServiceDesk Plus OnDemand