Switzerland is well known for it's outstanding public transport. You can travel to Lauterbrunnen SBB (swiss railways). And take from their either the BLM (Lauterbrunnen-Mürren) or from Stechelberg the Schilthornbahn. Tip: by an unlimited daypass for Switzerland, it gives you the transport to Mürren all-inclusive.
You will be able to drive by car either to Lauterbrunnen parkhouse. From here you will take the BLM via Grütschalp to Mürren.
Or you park at Stechelberg. Stechelberg is not covered and therefore cheaper. From here you take the Schilthorn bahn.
We are located a convenient 5-10 minutes walk to the BLM, and 10-15 minutes to the Schilthornbahn. Both stations can provide you with luggage cars. You only have to provide a deposit.
It is also possible to take a taxi in Mürren. Stäger transport can be called under +41 33 855 24 80