Ok my experience:
Im diving at least once a month with the bull shark (apparently the most agressive shark out there).
Ive also dived with hammerheads, ragged tooth, black tips and tiger sharks. Unfortunately never with the Great White (but will rectify it this year).
Specific your situation. We had some students in Mozambique in December on their first openwater dive. A tiger came to visit us. all of them just act normal and was an awesome experience for all of them (12 students). The point Im trying to make is that if you spot them underwater you will relise that they dont care about yiu at all. They come in have a look (if youre lucky and then dissapear.
Im alse a memebr of Sharklife and with experience and shark courses done I can comment as follow.
Key things to do if you not comfortable with the shark in the water and to scare them off And no jokes Im seriouse.
1) Stay in a group - they see you as one object too large for prey and they will not bother you.
2) If you alone swim towards the shark - a sure way to scare them off.
3) Never ever swim away horisontal from the shark - you look like food.
4) Stay vertical - no food of the shark swim vertical end they wont see you as prey
5) Blow a lot of bubbles and even scream if a shark is in you personal space (man how I would love that to happen to me)
6) Remember they hate to struggle for food and you do not look like easty pray to any shark in scuba. Swimmers on the syurface is another story - humans look clumsey make noice and look like you drown if you are a swimmer....
7) Eye contact very important, had a couple a csases where the bull shark comes in closer from behind and as soon as you look at it - it goes away.
8) Dont flash with your hands, keep them intack
Last point - onced you actually dive with these magnificant animals you quickly relise that they are no threat at all if you just respect them, dont hang on their dorsal fin and let them be.
I was in a dive with 50+ black tip sharks, and although they bump you by accident (because of the number of species and the feeding frenzie, they dont even notice you. Remeber their senses is super human and in 99.9999999999% of cases they will not mistake you with prey.
My few (very few) bad encounters with sharks, absolutely none of those worked. I think it is important to remember that a well fed shark is, for the most part, not a danger to anyone. However, a very hungry shark is a different story. If you dive in an area with lots of sharks, that means there is lots of food. But run into a desperately hungry shark, and all bets are off..
Bulls, by the way, vary tremendously in their aggressiveness, from one area to the next. Bulls in the Pacific off Panama are, for the most part, almost friendly... Bulls in the northern Gulf of Mexico can be very agressive. They also can be very timid.
If you ever get to dive with grey reef sharks, you should rethink your list, as only leaving will prevent a territorial attack.
Nice pictures by the way.