How to remove blue outline of select option in Twitter Bootstrap

Bootstrap form input elements do not use the outline property, but rather recreate it using box-shadow. You were on the right track with what you were doing, but the style that causes this is the following:

.form-control:focus {
    border-color: #66afe9;
    outline: 0;
    -webkit-box-shadow: inset 0 1px 1px rgba(0,0,0,.075),0 0 8px rgba(102,175,233,.6);
    box-shadow: inset 0 1px 1px rgba(0,0,0,.075),0 0 8px rgba(102,175,233,.6);
}

You will want to override those styles with your own, setting the box-shadow to none and adjusting the border-color to match your default.

As for the select box, you can use the following style, as was originally mentioned by @kamlesh-kushwaha, to override the bootstrap setting:

.bootstrap-select .btn:focus {
    outline: none !important;
}

For <select> dropdown, change in bootstrap-select.min line 29:

.bootstrap-select .dropdown-toggle:focus {
    outline: thin dotted #333 !important;
    outline: 5px auto -webkit-focus-ring-color !important;
    outline-offset: -2px;}

to:

.bootstrap-select .dropdown-toggle:focus {
    outline: none!important;
}

I remove bootstrap 4 dropdown-toggle 'on click' blue borders by doing this:

.yourdivname:focus {
  box-shadow: none;
}

Anything else seemed to be irrelevant. For instance, with normal buttons {outline: none} always seemed to work, but not for this element. All that was needed was the box-shadow:none property.