There's a possibility that Harry is calm and tries to reason with Dumbledore. He may think that there is a valid reason behind this and instead of panicking or getting angry, he uses his intelligence to communicate with Dumbledore, asking for an explanation and trying to find a solution to whatever situation Dumbledore believes is so dire.
Harry could also be angry. Despite understanding Dumbledore's generally good intentions, being tied to a bed against his will is a violation of his freedom. He might struggle against the restraints and demand to be released immediately, especially if he feels that Dumbledore is overstepping his boundaries.
Well, in the original storyline, Dumbledore is a very protective figure but would never take such an extreme and seemingly unethical action as tying Harry to a bed. This fanfiction clearly goes against the nature of their relationship as shown in the books. In the original, Dumbledore guides Harry with wisdom and respect, not through such forceful means.
One possible motive could be protection. Dumbledore might tie Harry to the bed to keep him from running off into danger. He has always been protective of Harry and perhaps in this fanfiction's unique scenario, he believes this extreme measure is necessary to safeguard Harry from some immediate and unseen threat.
He might be very sad at first. Harry has always valued his friends, so being forgotten by them would be a huge blow.
He might give Harry detention. Harry could be made to clean the trophies in the trophy room or help Hagrid with some difficult tasks in the Forbidden Forest under strict supervision.
It's also possible that Dumbledore has been misinformed or is under the influence of a dark spell himself. In the wizarding world, there are many forces at play. He could have received false information that made him think this was the best course of action for Harry. Another aspect could be that he is trying to teach Harry a lesson in a very extreme way. Maybe Harry has been too reckless, and Dumbledore wants to make him understand the seriousness of the situation.
In my opinion, Dumbledore would underestimate Harry Potter fanfiction. Fanfiction is a realm where fans take the original story and run with it in all kinds of directions. There are fanfictions that change the personalities of characters, create new storylines that deviate greatly from the original. Dumbledore, who is bound by the original narrative and his role in it, may not understand the significance of this new wave of creativity that fanfiction represents. He may see it as a distortion of the world he knows rather than a celebration and expansion of it.
Harry might initially be shocked and angry. He would probably struggle against the restraints and demand to know why Snape is doing this. He could yell at Snape, asking for an explanation and protesting his innocence if he believes he has done nothing wrong.
Well, Harry might outsmart Dumbledore by using his unique understanding of the magical world in ways Dumbledore doesn't expect. For example, Harry has a more direct experience with some dark magic items due to his encounters with Voldemort. He could use this knowledge to make decisions that seem counter - intuitive to Dumbledore but are actually more effective in a particular situation.
Harry would likely be deeply hurt. He has been through so much already, and this betrayal would be like another stab in the back. He might initially go into a state of shock, not believing that someone he loved could do this to him. Then, he would probably become very angry. His trust would be shattered, and he might lash out, not just at her, but also at those around him who he feels might have known or been involved in some way.
It might make Harry more confident. With Dumbledore's training, Harry gains more knowledge and skills, which gives him the confidence to face challenges.