I am looking to visit in June. One place we found was a house north one mile of San Pedro. Is it safe to walk from and too town at night? Also, I have heard that the bridge over the river is very narrow. Is this true?

Yes it is safe! Like anywhere else, don't walk home on a rum overdose at two a.m., flashing your wallet.
The bridge has two lanes, each of them wide enough for a golf cart/ ATV.

BS, It is quite dark to be walking at night north of the cut. You can however ride the island ferry (Cheap) from say the palappa bar (should be close to one mile north) to fido's (Pronounced feedos) dock in town . They will drop you back at the palappa bar dock or possably one closer to where you are staying (if the water is not too low). So no need to walk in the dark. There phone # is listed in the book or just stop by there office on Fido's dock and they will give you a card with the phone # and schedule for the boats. the bridge is plenty wide (a truck could drive over it if they allowed it to) and brand new , no problem with going over the bridge.

Are you one mile north of town or one mile north of the cut?
Distances here are usually measured from Central Park in town, so one mile north of town is not necessarily one mile north of the cut.
If you are one mile north of the cut, you will be at the Tres Cocos area which is beautiful, but not always a cool place to walk alone in the middle of the night.
Rent a golf cart ($BZ 10.00 roundtrip over the toll brigde) or follow 2mile's advice and use the Island Ferry (226-3231).

We just got back from San Pedro yesterday. We stayed right past the cut in Reef Village Condos and felt safe the entire time. However, it's QUITE dark and the road very rough past the bridge. In fact, due to lots of construction, there was water running over the "road" (dirt) which could create a whole other set of issues. Past the palapa bar, the road got almost impossible, with HUGE mud holes and ruts. In fact, we got our golf cart stuck and had to wait for someone to help pull us out. I hope you are staying south of those unless you plan on getting to your house by boat. Aside from this, it was wonderful and everyone was very nice. As I said, we never had anyone make us feel uncomfortable. Have fun!!! We hope to go back next year!