Bootstrap full-width text-input within inline-form

The bootstrap docs says about this:

Requires custom widths Inputs, selects, and textareas are 100% wide by
default in Bootstrap. To use the inline form, you’ll have to set a
width on the form controls used within.

The default width of 100% as all form elements gets when they got the class form-control didn’t apply if you use the form-inline class on your form.

You could take a look at the bootstrap.css (or .less, whatever you prefer) where you will find this part:

.form-inline {

  // Kick in the inline
  @media (min-width: @screen-sm-min) {
    // Inline-block all the things for "inline"
    .form-group {
      display: inline-block;
      margin-bottom: 0;
      vertical-align: middle;
    }

    // In navbar-form, allow folks to *not* use `.form-group`
    .form-control {
      display: inline-block;
      width: auto; // Prevent labels from stacking above inputs in `.form-group`
      vertical-align: middle;
    }
    // Input groups need that 100% width though
    .input-group > .form-control {
      width: 100%;
    }

    [...]
  }
}

Maybe you should take a look at input-groups, since I guess they have exactly the markup you want to use (working fiddle here):

<div class="row">
   <div class="col-lg-12">
    <div class="input-group input-group-lg">
      <input type="text" class="form-control input-lg" id="search-church" placeholder="Your location (City, State, ZIP)">
      <span class="input-group-btn">
        <button class="btn btn-default btn-lg" type="submit">Search</button>
      </span>
    </div>
  </div>
</div>