Hi Emilia,
Alas, REST endpoint of the Route solver does not allow clients to change the default snap tolerance. Is you still think you need to do this, you can try doing it through SOAP, or another option would be a GP service. In the former case the things get complicated as there is now out of the box JavaScript SOAP client; in the later case - GP services are slightly slower than NAServer ones.
But I'm also curious - why do you need to change the snap tolerance? Is there a problem with accurate locating of the bridges on the network?
thanks,
Dmitry