Table Relationship - One to Few (Many)
The compound PK of EmployeeId and AddressTypeId is exactly what you want, and you don't need anything else. The relationship is still a one-to-many relationship, as for one employee, you may have many address whether it is a home address or a work address.

The bridge table is interesting if you may have the same address for multiple employees AND that a same address may be of a different type for multiple employees. If it's not the case, this table is pretty overkill and may add more complexity for nothing.

TL:DR: First solution is probably the best.