They literally didn't burn down the bridge (that would be a plot twist!), but in the metaphorical sense that they are eliminating all ties to something. With the house, they are burning all of their belongings, which included family sentiments and memorabilia. These are all reminders and ties to the past and to their life there, while the house itself is the anchor. By burning it all, they are effectively severing all ties with Fingerbone as a place. The house not actually ending up burning down is besides the point; it's the act that really counts. The second part of "burning the bridges" is the crossing of the bridge. By crossing the bridge, they go to a place where the inhabitants of Fingerbone will never go, leaving them behind. With this, Ruth and Sylvie cut all ties with the people of Fingerbone. Their supposed deaths only solidify this truth; to Fingerbone, Ruth and Sylvie are now ghosts, taken away by the lake never to be found again like many before them. At this point Fingerbone has no more ties with Ruth and Sylvie apart from it being a place where they had once been, all bridges burned down now free to do whatever they want.
(Side note, couldn't help but think these lyrics fit the post and moment perfectly, so here they are)
"Gather in the ashes (Your bridges are burning down)
Everything thrown away (They're all coming down)
Gather in the ashes(It's all coming round)
Everything thrown away (They're all coming down)
Gather in the ashes(It's all coming round)
Scatter as they blow away"
- Foo Fighters, "Bridge Burning"