I can't provide details about the hotel, as I haven't stayed there. I can provide information about walking.
First, here's the orientation of the various Disney Springs Hotels:
According to Bing Maps, the distance from the Marketplace section (shown as "Downtown Disney" on my old map) to the B Resort and Spa is about 2,900 feet (880 meters). That's 0.55 miles (0.88 km).
Link to Bing Maps:
https://binged.it/2IgS60U
Like all areas of Disney World, the area around the Disney Springs Hotels can be considered very safe. There are almost always cars running along Hotel Plaza Blvd. The likelihood that anything bad will happen is low. If you remain aware of your surroundings, you'll be fine.
Important: I've stayed dozens of nights at Disney Springs Hotels over the past several years. I'm mostly nocturnal, so I've walked alone between Disney Springs and various hotels many, many times. I've never once felt anything remotely sketchy. That said, I'm not a woman. I've also lived in "dodgy" neighborhoods in both Minneapolis and Fort Lauderdale. My threshold for what I consider safe might be different than other people.
Alternative to Walking
The Disney Springs Hotels runs a bus route that runs between the hotels and Disney Springs. It starts at 6pm and runs every 30 minutes, with the last pick up at 3am. That bus will drop you off right at your hotel.
The pick up point at Disney Springs is the West Side Transfer Station. That's past the Cirque du Soleil theatre and House of Blues. Although it's a bit remote, every times I've been in that area waiting for the bus, I've seen Disney Security. I guarantee that if you approach any Disney Security officer and ask, she or he will escort you (or find someone who will) to the bus stop. And she or he will almost certainly wait until the bus arrives.
Location Compared to Disney Springs Neighborhoods:
Link to Bing Maps:
https://binged.it/2IeN6d7
