If you have problems connecting to a multiplayer session of Bloodborne, Sony published a few pointers on how to smooth things out.
First of all, make sure that the NAT type on your PS4 isn't 3 by doing a connection test. If it is, you might not be able to connect to the PSN services at all (this isn't just related to Bloodborne, mind you, but to the PSN in general).
Solving the NAT 3 problem is slightly laborious, but doable. You can find a handy guide here.
If your NAT type is 1 or 2, and you're still encountering problems, you might want to manually open the following ports on your router:
Ports required to connect to the PSN:
- TCP: 80,443,3478,3479,3480,5223,8080
- UDP: 3478,3479,3658
Ports required to play online on Bloodborne:
- TCP: 18671, 20443
In order to open your ports, you need to assign a static IP to your PS4 (following the guide linked above), and then follow the instructions related to your own router that you can find here.