Using Bootstrap modal instead of DayPilot Modal

Yes, this is no problem. The DayPilot Modal is just an optional helper.

This example shows how you can use DayPilot.Modal to ask for description when creating a new event:

  onTimeRangeSelected: function (args) {
    var dp = this;
    DayPilot.Modal.prompt("Create a new event:", "Event 1").then(function(modal) {
      dp.clearSelection();
      if (!modal.result) { return; }
      dp.events.add(new DayPilot.Event({
        start: args.start,
        end: args.end,
        id: DayPilot.guid(),
        resource: args.resource,
        text: modal.result
      }));
    });
  },

You can see that it's not hardwired and you can easily replace it with any other modal dialog implementation. The same applies to editing (see the onEventClick event).

Let me know if it doesn't help.