Bootstrap Table json from ajax

check this Fiddle

you must specify the data-field in each th also you must remove the data-toggle="table"

data-toggle="table" as documentation : Activate bootstrap table without writing JavaScript. Set data-toggle="table" on a normal table.

in your case if you don't want to use javascript just do your table as below

<table data-toggle="table" class="display table table-bordered" data-url="php/process.php?method=fetchdata">
    <thead>
        <tr>
            <th data-field="Nome">Nome</th>
            <th data-field="Cognome">Cognome</th>
            <th data-field="DataN">Data Nascita</th>
            <th data-field="Provincia">Provincia</th>
            <th data-field="Comune">Comune</th>
            <th data-field="CAP">CAP</th>
            <th data-field="Indirizzo">Indirizzo</th>
            <th data-field="Fisso">Fisso</th>
            <th data-field="Mobile">Cellulare</th>
            <th data-field="Note">Note</th>
        </tr>
    </thead>
</table>