Can I ask the tenant to cover some of the costs of the extermination of bed bugs since I believe they brought them in?

The tenant is not responsible for any costs unless the landlord can prove that the tenant willfully or negligently failed to co-operate in their efforts to eradicate the bugs. The landlord would have to issue the tenant an N5, and file an L2 application with the LTB to recover the costs. Consult with a legal representative before you give a legal notice of termination to your tenant.