You should be able to book for all persons but it showing only for ONE person MEANS you need to CHECK infotype 2001 and his workschedule. If it showing for all the persons, just follow as below:
Create a calendar with open days means without any holidays and assign in Training and Event Management --> BASIC Settings --> Controling days off --> Specify FACTORY Calendar in this through drill down/check box select the calendar which you have created in time mangement without any holidays and try out if again. If it shows the same message then remove time integration.

You should be able to book for all persons but it showing only for one person means you need to check infotype 2001 and his workschedule. If it showing for all the persons, just follow as below:
Create a calendar with open days means without any holidays and assign in Training and Event Management --> Basic Settings --> Controling days off --> Specify Factory Calendar in this through drill down/check box select the calendar which you have created in time mangement without any holidays and try out if again. If it shows the same message then remove time integration.