owl carousel 2 not work with loop and 1 items (Bug Fixed Now)

You could check the number of .item elements before you call your plugin like so:

// Be more specific with your selector if .items is used elsewhere on the page. 
var items = $('.items');
if(items.length > 1) {
    $('#owl-demo').owlCarousel({
        loop: true,
        ...
    });
} else {
    // same as above but with loop: false;
}

I report this bug to Owl developer group and fix this problem here.

Change this line in Commit

view = Math.max(settings.items * 2, 2),

Now this worked in demo

I hope the below method will solve your problem.
You dont need to edit the owl carousel js. The same method can be applied to Bx Slider also.

$('.owl-demo').owlCarousel({
    margin: 0,
    responsiveClass: true,
    smartSpeed: 500,
    dots: ($(".owl-carousel .item").length > 1) ? true: false,
    loop:($(".owl-carousel .item").length > 1) ? true: false,
    responsive: {
        0: {
            items: 1,
        },
        500: {
            items: 1,
        },
        768: {
            items: 1,
        }
    } 
})