Booking limitation with check SQL - mysql

Question

I want to set a constraint where a person IS NOT ALLOWED TO book a certain car, if it is already booked. I'm a bit of a beginner therefore I wonder if check/trigger would be an idea for this problem. E.g.
ALTER TABLE bookings
ADD CHECK (vehicle_id = NOT NULL)
The tables are
CREATE TABLE customers (
customer_id int(50) NOT NULL AUTO_INCREMENT,
fname varchar(20) NOT NULL,
lname varchar(20) NOT NULL,
dateOfBirth date NOT NULL,
address varchar(30) NOT NULL,
city varchar(20) NOT NULL,
county ENUM('Armagh','Carlow','Cavan','Clare','Cork','Derry','Donegal','Down','Dublin','Fermanagh','Galway','Kerry','Kildare','Kilkenny','Laois','Leitrim','Limerick','Longford','Louth','Mayo','Meath','Monaghan','Offaly','Roscommon','Sligo','Tipperary','Tyrone','Waterford','Westmeath','Wexford','Wicklow') NOT NULL,
phone int(10) NOT NULL,
email varchar(20) NOT NULL,
payment_method ENUM ('Visa', 'Amex', 'Cash', 'American Express', 'Mastercard') NOT NULL,
valid_licence varchar(5) NOT NULL,
status varchar(10),
PRIMARY KEY (customer_id)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;
CREATE TABLE vehicles (
vehicle_id int(10) NOT NULL AUTO_INCREMENT,
category ENUM('Sedan','Hatchback','SUV', 'Coupe', 'Crossover') NOT NULL,
no_of_seats int(11) NOT NULL,
brand varchar(20) NOT NULL,
model varchar(20) NOT NULL,
product_year int(5) NOT NULL,
rate_per_day int(11) NOT NULL,
PRIMARY KEY (vehicle_id)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;
CREATE TABLE vehicle_collections (
collection_id int(10)NOT NULL AUTO_INCREMENT,
vehicle_id int(10) NOT NULL ,
collection_date date NOT NULL,
return_date date NOT NULL,
mileage_before int(10) NOT NULL,
mileage_after int(10) NOT NULL,
duration int(5) NOT NULL,
PRIMARY KEY (collection_id),
KEY vehicle_idfk1 (vehicle_id),
CONSTRAINT vehicle_idfk1 FOREIGN KEY (vehicle_id) REFERENCES vehicles (vehicle_id)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;
CREATE TABLE bookings (
booking_id int(50) NOT NULL AUTO_INCREMENT,
booking_date date NOT NULL,
start_date date NOT NULL,
end_date date NOT NULL,
invoice_no int(10) NOT NULL ,
chauffeur_id int(10) NULL,
vehicle_id int(10) NOT NULL ,
customer_id int(50) NOT NULL ,
chauffeur_req ENUM('Yes','No') NOT NULL,
special_instructions varchar(255) NOT NULL,
PRIMARY KEY (booking_id),
KEY invoice_nofk2 (invoice_no),
KEY chauffeur_idfk1 (chauffeur_id),
KEY customer_idfk2 (customer_id),
KEY vehicle_idfk2 (vehicle_id),
CONSTRAINT invoice_nofk1 FOREIGN KEY (invoice_no) REFERENCES invoice (invoice_no),
CONSTRAINT chauffeur_idfk2 FOREIGN KEY (chauffeur_id) REFERENCES chauffeurs (chauffeur_id),
CONSTRAINT customer_idfk3 FOREIGN KEY (customer_id) REFERENCES customers (customer_id),
CONSTRAINT vehicle_idfk3 FOREIGN KEY (vehicle_id) REFERENCES vehicles (vehicle_id)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;
Here is my table structure if it will help. I think of using a check but one of main problems is - How do you say in MySQL language that ' if a car is booked?' . Trigger?