how to hide one column from grid in bootstrap mobile version

Since Bootstrap V4 the hidden-X classes have been removed. In order to hide a column based on the column width use d-none d-X-block. Basically you simply turn off the display of the size you wish to hide then set the display of the bigger size.

• Hidden on all .d-none
• Hidden on xs .d-none .d-sm-block
• Hidden on sm .d-sm-none .d-md-block
• Hidden on md .d-md-none .d-lg-block
• Hidden on lg .d-lg-none .d-xl-block
• Hidden on xl .d-xl-none

Taken from this answer.

Since, you are hiding the second column in "xs", you can use the full width for the first column by defining the class "col-xs-12" to column1.

<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap.min.css" rel="stylesheet"/>
<div class="row">
  <div class="col-xs-12 col-sm-9">
    <p class="testimonial-about">"We have managed to received good number of applications through MyJobs in comparison to advertising in the newspaper and would recommend MyJobs to other companies to assist with their recruitment needs"</p>
  </div>
  <div class="col-sm-3 center-image hidden-xs"><img src="myimage.png"/></div>
</div>

If you are using bootstrap 4, and/or want to hide a column on anything other than extra small view, here is how:

Bootstrap 3:

<div class="row">
  <div class="col-lg-12 col-xl-9">       
  </div>
  <div class="col-xl-3 hidden-lg hidden-md hidden-sm hidden-xs">
  </div>
</div>

in other words you have to define every single individual predefined viewport size you want the column to be hidden in.

Bootstrap 4: (a little less redundant)

<div class="row">
  <div class="col-lg-12 col-xl-9">       
  </div>
  <div class="col-xl-3 hidden-lg-down">
  </div>
</div>

Also, if you want to hide a column if the screen is too big:

<div class="row">
  <div class="col-md-12 col-sm-9">       
  </div>
  <div class="col-sm-3 hidden-md-up">
  </div>
</div>

also note that col-xs-[n] has been replaced by col-[n] in bootstrap 4