It’s driving me nuts just to implement custom google search box into my website.
Because bootstrap overide the CSS, so here’s the solution
Get your Google Custom Search here https://www./cse/

You need to override the box sizing for some of these external tools. Wrap them in a class (as shown below) or reset it on the individual elements.

.reset-box-sizing,
.reset-box-sizing * {
  -webkit-box-sizing: content-box;
     -moz-box-sizing: content-box;
          box-sizing: content-box;
}

Place this code in your desire page, don’t forget to Insert your own Custom Search engine ID

In your CSS

.reset-box-sizing,
.reset-box-sizing * {
  -webkit-box-sizing: content-box;
     -moz-box-sizing: content-box;
          box-sizing: content-box;
}