First and foremost, to answer your question of the differences
between a bridge and access point...
Network bridging in layman term refers to connecting 2 or more
segments of a network together. Bridging happens between networking
devices such as router to bridge, and bridge to access point. These
days, standalone network bridge has less popular as routers and
access points have included network bridging features into them,
except for some very specialized functions.
A wireless access point is a network device that allows
computers and smartphones to connect to a network via Wifi or other
wireless technologies. An access point can be a standalone device
or forms part of a router.
Now...what should you get for Room B?
You will need an access point to bridge the wifi network in Room
A and propagates the signal to Room B.
If I were you, I will never go for Linksys. But if you insist on
Linksys, you can consider using RE1000 for your Room B. Ideal
placement for Linksys RE1000 would be: