You can easily check where libb.so is expected to be with ldd command:
 $ ldd liba.so
    linux-gate.so.1 =>  (0xb77b0000)
    libb.so.1 => not found
    libstdc++.so.6 => /usr/lib/libstdc++.so.6 (0xb75b6000)
    libgcc_s.so.1 => /lib/libgcc_s.so.1 (0xb7572000)
    libc.so.6 => /lib/i686/cmov/libc.so.6 (0xb742b000)
    /lib/ld-linux.so.2 (0xb77b1000)
If it's not found, libb.so's path should be added to /etc/ld.so.conf or shell variable LD_LIBRARY_PATH.
Another way is setting rpath in the liba.so itself - it's basically hardcoding its path so when the binary is started the dynamic linker would know where to search for the shared libraries.
If rpath is not set it will first search in LD_LIBRARY_PATH, then the paths mentioned in /etc/ld.so.conf (or /etc/ld.so.conf.d/). After adding to ls.so.conf don't forget to execute /sbin/ldconfig
Dynamic linker searches the dependent shared libraries by their soname (if it's set) - if soname is not set (with -Wl,-soname,libb.so.1 for example), it will be searched by library's name.
Example: libb.so.1.0 is your actual library, having soname - libb.so.1. You would normally have the following files structure:
libb.so -> libb.so.1
libb.so.1 -> libb.so.1.0
libb.so.1.0
where libb.so and libb.so.1 are symlinks.
You usually link to libb.so, when building some application or other library, depending on libb.so. 
gcc -shared -Wl,-soname,liba.so.1 -o liba.so.1.2 -L/libb/path -lb
When the application is started (or dlopen is executed - your case)  - the dynamic linker will search for file with name libb.so.1 - the soname of dependent library, if the soname is set, not libb.so.
That's why you need that symlink libb.so.1, pointing to the actual library.
If you use ld.so.conf and ldconfig, it will create the symlink with soname's name, pointing to the library file, if this symlink is missing.
You can see ld-linux man page for more useful info.
If the library is found but some of the symbols are missing, try building 
libb.so with 
-Wl,--no-undefined option
gcc -shared -Wl,-soname,libb.so.1 -Wl,--no-undefined -o libb.so.1.2
It should give you an error if you missed to define some symbol.