The result of
$table.bootstrapTable('getSelections')
is just a plain old JavaScript object. It's not JSON. There is no need to stringify it. Stringification is for turning an object into a string in order to store it or send it somewhere. That's not what you want to do. Just access the value you want directly from the JavaScript object:
var data = $table.bootstrapTable('getSelections');
data[0].name
If you unnecessarily stringify this response as you are doing, then you're just going to have to turn around and parse it again, as your "accepted" answer incorrectly suggests, which will do nothing more than give you back the object you started with in the first place.
.stringify()if you want to get values from the data?