Usual RS485 gotchas:
1) RS485 is a three-wire bus. Ground (or return) wire is absolutely mandatory. Some devices use mains protective earth as RS485 ground, which is confusing and usually causes EMC/EMI failure, but communication still often works even with such designs; but if you don't have even that, but have completely floating grounds, it's likely not going to work at all.
2) Additionally to termination (the need of which is probably well known even to young players), you also need biasing. Termination resistors are used twice (once at each end of the bus); biasing resistors are used once at the bus (where exactly does not matter, but often at master). Google for "RS485 fail-safe biasing" for application notes how to calculate them, but do note the name is absurd, fail-safe biasing has absolutely nothing to do with fail-safe, it's a normal operational requirement.
3) Note how there are two differing ways to label A and B; basically Wikipedia + a few others, versus most of the manufacturers. There is still enough disagreement about what the standard originally meant and who is right and who is wrong, so that only practical way is to always test swapping these two signals until the communications work. If you need to try out other parameters, too, this doubles the number of permutations; for each experiment you make, you need to test it with A&B swapped and non-swapped.
Your way of finding the shortest bit and measure it's period seems correct to me. Expect to see any weird baud rates in RS485 systems. And also any stop bit and parity settings. And remember that even if a standard such as the modbus standard says something about the required parity setting, that does not mean anyone follows these requirements.