New to Java Programming - Any Feedback?

A number of points:

• Do not use floating-point data types (float or double) for amounts of money. Floating-point data types have limited precision, they cannot represent all decimal values exactly, and you're going to get roundoff errors sooner or later. Use integers instead (int or long) and store cents instead (for example, 1040 cents) or use BigDecimal.
• Make member variables private by default; only make them protected (or another access level) if there is a good reason to do so.
• Prefer local variables above member variables. Is there a good reason why s is a member variable instead of a local variable?
• Don't write the main part of a program in the constructor of a class. You have the main part of your program in the constructor of the Bank class. The constructor is meant to initialize the state of a new object, so the only thing that the constructor should do is initialize member variables.
• In your constructor, you catch an InputMismatchException and print an error message ("bye bye...") but you are not actually returning from the constructor. So execution will continue and print "Incorrect PIN entered ..." which is not what you meant.
• The program doesn't actually do what you'd expect it to do; withdrawal, deposit etc. functionality never gets called anywhere.
• You need a public static void main(String[] args) method to be able to run this as a stand-alone program.

Jesper has already made comments on the code itself, so I will address your organization. You only have one big class that does everything, and it does things in many areas. For instance, your class handles customers, accounts, and security. You should split these out into separate classes. Perhaps Bank would be your top level class, with the main method. Then you would have an Account class, with the withdraw, deposit, and checkBalance methods, a Customer class with a list of accounts that customer has as well as methods for checking their credit rating, etc.

Security - your model is weak, but obviously this is an exercise so let's keep it simple (and I'm no security expert either!). I'd create a file with the credentials for each customer, and have a class used for authenticating the user before you do anything, say Authenticator.

Authenticator auth = new Authenticator();
Customer cust = null;

while (cust == null) {
   System.out.println("Username: ");
   String username = s.nextLine();
   System.out.println("PIN: ");
   int pin = s.nextInt();

   cust = auth.authenticateCredentials(username, pin);
}

The authenticateCredentials() method would return null if the credentials provided did not match any on record. If a match was found, it would return the customer records that match the login credentials.

Obviously I'm leaving a lot out, like how to save the customer and login information, and organizing the relationship between customers and accounts. I'd recommend that you take a peek at the ArrayList class for keeping lists of accounts. You've got a good start here, with a lot you can do to improve and add new features. Have fun on the new project!

I would say instead of:

if (pin != PIN) {
        System.err.println("Incorrect PIN entered, please try again later.");
        System.exit(0);
    }
    access = true;

use :

if(pin == PIN){
   access = true;
    System.out.println("Welcome to JCBank please choose from the following options");
    System.out.println();
    System.out.println("Withdraw (1)\tDeposit (2)\tCheck Balance (3)\tApply for Loan(4) \tQuit (5)");
    System.out.println();
}
else{
    System.err.println("Incorrect PIN entered, please try again later.");
    System.exit(0);
}

its much more readable I guess.