Two notes:
1) I use Connection not just ion terms of "What can this Contact do" but also "What
will this contact do." I realize that overlaps with loyalty some, but for some contacts, even though they should have a higher connection rating, I cap them based on where their personal and professional limits are. You may be their best friend, and they may be willing to take a bullet for you, but they're not going to sell out their country/corp/whatever for you.
There's also a little bit of a balancing factor there too.
Plus, you will never see a "6" contact rating in Missions. That's Lofwyr, Fastjack, Nadja Davier level of Connections. 6 should be very, very rare. (Honestly, the ratings should go higher, but since they stop at 6...)
Bull's connection rating is a 5 not so much because of him, but because of his extended contacts. Bull can pull in Jackpoint if necessary. He can call on Fastjack. And considering how personal some of the Missions are to him, it made sense for him to have a 5.
2) Tosh is not actually head of a task force charged with capturing Shadowrunners. He's on a floating, Special Crimes task force. His job is to handle anything major that crops up. Frankly, Shadowrunners are not too often a major crime problem for the city. For corps, yes. but the city? Not as often. Tosh's focus is gangs, the mob, and whatever major crime problem is making the news and causing problem for the city and the DA's office. Keep in mind he got this gig by catching a serial killer that had been terrorizing the city for 3 years.
that said, play him up how you like.
It's all fun
Bull