Hey 
Welcome to the Bubble community! I believe you can do what you are looking to do in Bubble. There are probably many ways to do this. I’m not at my computer right now but let me see if I can give you some links at least. Here are a few examples of how you could do the scheduling part of it.
Preview: Help building availability System! Willing to Pay
Also, displaying the calendar that way should be possible as well by making a customer calendar like this: [HOW-TO] Create a custom Calendar using repeating group
Another way: New Plugin - Calendar Tool (free)
And a different way: https://bubble.io/plugin/calendar-grid-pro-1554923664903x211854095567290370
Hope that helps! 
For All Your No-Code Education Needs:
- One-on-One Tutoring
- eLearning Hub
- Video Tutorials
- No-Code Classes