My approach to tabular data is to use a table.

The grid that Bootstrap uses is suitable for the structure of a web-site so that it responds to the various devices and resolutions without major headache for the programmer.

Regarding the presentation of information, you should use markup that corresponds to the type of information to be presented. We have to keep in mind the applications that collect data based on markup in use in order to assist users.

Final score

Demonstration in JSFiddle

You can reduce and increase the width of the preview window of JSFiddle to see the information to be adapted to the existing space.

HTML

For HTML, I have tried to use the least possible markup but at the same time ensure that in the various devices we will have homogenous behavior.

My solution is to have a container ( .container ) with a line ( .row ) and a column that occupies the entire width of the container ( .col-md-12 ) so that we have a grid that adapts and responds to screen resolution changes.

Inside the column we have a header and a table with the data to display:

<div class="container">
    <div class="row">
        <div class="col-md-12">

            <h5 class="app-header text-center">
                <strong>Núcleo Regional da Diretoria de Araguaína</strong>
                <br />
                (mock,  mock,  mock,  mock,  mock,  mock,  mock)
            </h5>

            <table class="app-table-info">
                <thead>
                    <tr>
                        <th colspan="3" class="text-center">
                            Plantão
                        </th>
                    </tr>
                </thead>
                <tbody>
                    <tr>
                        <td rowspan="2">
                            Defensor Público:
                            <br/>
                            <strong>Fabricio Silva Brito</strong>
                            <br/>
                            Servidor:
                        </td>
                        <td>
                            Período
                        </td>
                        <td>
                            Telefone
                        </td>
                    </tr>
                    <tr>
                        <td>
                            Início 07/03 as 18h00
                            <br/>
                            Término 07/03 as 18h00
                        </td>
                        <td>
                            (92) 3232-3232
                        </td>
                    </tr>
                </tbody>
            </table>
        </div>
    </div>
</div>

CSS

For CSS I have created classes with the prefix app- so they are perfectly distinct from any other class Bootstrap uses. This way you know when a style of yours is being applied or subscribed by framework :

/* Cabeçalho Verde */
.app-header{
    background: #178F8D;
    color: #fff;
    line-height:1.4em;
    padding:5px 0;
    margin-bottom:20px;
}

/* Tabela com Informações */
.app-table-info{
    background: #E6E7E9;
    color: #3A3A3A;
    width:100%;
}
.app-table-info th,
.app-table-info td{
    padding:10px;
    border-bottom:6px solid #fff;
}
.app-table-info th{
    background: #BEBFC1;
    color: #178F8D;
}
.app-table-info td{
    height:60px;
}
.app-table-info tr:first-child td:first-child{
    vertical-align:top;
    border-right:6px solid #fff;
}
.app-table-info td:last-child{
    border-left:6px solid #fff;
}

Hello, I just did not insert the blank spaces, because at the moment I do not have a publisher of my own, and I really forgot to insert them manually.

<div class="block">
        <div class="row">
            <div class="block_header">
                <b>Núcleo Regional da Diretoria de Araguaína</b><br>
                (mock,  mock,  mock,  mock,  mock,  mock,  mock)
            </div>

            <div class="block_subheader">
                <b>Plantão</b>
            </div>


            <div class="col-md-4 info">
                Defensor Público:<br>
                <b>Fabricio Silva Brito</b><br>
                Servidor:<br>

            </div>

            <div class="col-md-4 info">
                <table>
                    <tr>
                        <th>Período</th>
                        <th>Telefone</th>
                    </tr>    
                    <tr>
                        <td>Início 07/03 as 18h00<br/>
                            Término 07/03 as 18h00</td>
                        <td>(92) 3232-3232</td>
                    </tr>    
                </table>    

            </div> 

        </div>

CSS looks like this:

  .block_header{
background: #178F8D;
color: #fff;
padding: 5px;
text-align: center;
margin: 3px;

}

  .block_subheader{
background: #BEBFC1;
color: #178F8D;    
text-align: center;    
padding-bottom: 10px;
margin-top: 20px;

}

  .info{
background: #E6E7E9;
color: #3A3A3A;
margin: 0px 5px 5px 0px;
padding: 5px;
height: 100%;
float:left;

}

   .separator{
padding: 0px 0 23px;
float:left;

}