Developing a JavaScript library
Not "stupidly bad", but you're invoking .push() far more times than needed. It's a variadic function, so group the items into single invocations.

Additionally, I'd probably put a toString() method on the BatchInfo.prototype that will give back the string representation of the object.

Then put the objects directly into what was the batchString array. That way the .toString() method will be invoked when you call .join().

I've included additional small changes below as well.

(function () {
    var info = [],
        b = {
            clear: function () {
                info.length = 0; // Clear all references
            },
            get: function () {
                return info;
            },
            add: function (command, url, data) {
                info.push(new BatchInfo(command, url, data));
                return info;
            },
            toString: function () {
                // Put the `BatchInfo` objects directly into the Array.
                // Now we don't need the `for` loop.
                return ['--batchfull',
                        'Content-Type: multipart/mixed; boundary=batchitems']
                           .concat(info).join('\r\n'); // Not needed-- || '';
            }
        };
    function BatchInfo(command, url, data) {
        this.URL = url || '';
        this.Command = command || '';
        this.Data = data || '';
    }
    // Handle the `toString()` representation here
    BatchInfo.prototype.toString = function() {
        var parts = ['', '--batchitems',
                     'Content-Type: application/http',
                     'Content-Transfer-Encoding: binary',
                     '',  this.Command + ' ' + this.URL + ' HTTP/1.1'];

        if (this.Command !== 'DELETE') {
            parts.push('Content-Type: application/json;type=entry');
        }
        parts.push('', this.Data);
        return parts.join('\r\n');
    };
    function BatchCacheRequest(info, description) {
        this.Info = info || '';
        this.Description = description || '';
        this.SubmitDateTime = new Date().toString('yyyy-MM-dd HH:mm');
    }
    window.batch = b;
})();