Not getting wordpress nonce to work with wp-rest api application

According to the docs:

For developers making manual Ajax requests, the nonce will need to be passed with each request. The API uses nonces with the action set to wp_rest. These can then be passed to the API via the _wpnonce data parameter (either POST data or in the query for GET requests), or via the X-WP-Nonce header.

The important part you are missing is:

The API uses nonces with the action set to wp_rest.

For it to work, you must name your action in the wp_create_nonce to wp_rest.

So for your code, you must change all instances of:

wp_create_nonce( "a" )

to

wp_create_nonce( 'wp_rest' )

Also, as the docs state:

Supplying the nonce as a header is the most reliable approach.

So adding this to your ajax is simple and looks something like:

var _nonce = "<?php echo wp_create_nonce( 'wp_rest' ); ?>";$.ajax({    type: 'POST',    url: url_path + '/foo/v1/newbee',    data: {        bid : next    },    dataType: 'json',    beforeSend: function ( xhr ) {        xhr.setRequestHeader( 'X-WP-Nonce', _nonce );    }});

Also, to fix the check

check_ajax_referer( 'a', $nonce, false )

Should now be

check_ajax_referer( 'wp_rest', '_nonce', false )