Can you get bed bugs by using a washing machine that was used by someone with bedbugs?

In theory, yes. The hot water is not sufficient to kill bed bugs, so if any remain in the clothing after the spin cycle but are left behind when clothes are removed, the next user could acquire them. The second user would have to super-dry their clothes (high heat, 40 minutes after completely dry) to kill the newly acquired bedbugs.

In practice, no, it is extremely unlikely that any bugs would remain in the machine after multiple rinses and spin cycle.