JSFiddle - React, Tailwind, and code Playground

HTML

<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap.min.css">
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/js/bootstrap.min.js"></script>
<div class="col-xs-6" style="background-color: grey">
  Irrelevant div
</div>

<div class="col-xs-6 text-center" id="signUpForEarlyAccess">
  <div class="fully-centered">
    <h3 contenteditable="true">Sign Up for Early Access</h3>
    <h5>Enter your email to be one of the first to try!</h5>
    <div class="form-group input-group">
      <input id="emailForm" placeholder="Please enter an email address" type="email" class="form-control">
      <span class="input-group-btn">
                    <button type="submit" class="btn btn-success">Sign up</button>
                  </span>
    </div>
  </div>

CSS

#signUpForEarlyAccess {
  float: right;
  background-color: #F8F8F8;
  border:1px solid red;
  display:flex;
  align-items:center;
  justify-content:center;
  align-content:center;
  height:250px;
}

.fully-centered {
  position: relative;
}