Is using a tasbih haram/bida'ah?

There's no issue with using a tasbih. It's not bida'ah at all. What it does is it helps to facilitate the act of dhikr, remembering Allah subhanahu wa ta'ala. So, for example, after you finish praying, you could say subhanAllah 30 times, alhamdulillah 30 times, allahu akbar 34 times, various different narrations. Now, in terms of the bida'ah aspect, that comes when you're introducing something new to the religion. This isn't something new. This is something there which helps facilitate an already established act of the sunnah of the Prophet Muhammad . The same, for example, for maybe microphones. It's not a new act. You're using it to help facilitate an already established act. Let's say the adhan in this case. So there's no issue with it. If you want to use your hands, then some could say that your hands are better, specifically because each part of your finger will testify for you. So, yes, that's it. That's maybe what one would say is best. But it's not bida'ah in any way, shape or form to use a tasbih.