YABU
There are many different kinds of bonus, which I think is influencing a lot of peoples' responses - performance based, contractual, discretional, gift etc - and the response and "obligation" to thank for each one would be different.
A performance based and/or contractual bonus I don't think needs a thank you - it is based on you hitting your targets and is agreed as part of your renumeration package for doing the job.
A discretional bonus, based on good reviews/going above and beyond, I think I would send an email/note to whoever was in charge of that decision (so whether it was my supervisor, the manager or the big boss) to show my appreciation for the gesture.
A gift that had no bearing on my work, eg just because it was Christmas and the boss was giving everyone the same gift - monetary or otherwise - would get a thank you from me, just like any other gift would. However, since a gift is supposed to be given without obligation, you can feel disappointed/upset that the recipients haven't said thank you, but to actually consider their employment statu based on it, is out of order IMHO.
All of this is tempered by the assumption that I am not handed the cheque/money directly. If I was, then I would thank whoever was giving it to me out of pure courtesy, if nothing else.
TL:DR There is no obligation to say thank you for a bonus but it is polite to do so, and people shouldn't have to worry that their "position in the company" would be under review based on how grateful they appeared to their boss.