Bells are not required by law to be put on new adult bicycles when sold, they are however required on bikes for kids, and at least one company, the Electra puts them on for adult bikes too, but you won't find them on adult bikes. Reflectors on the other hand are required on all bikes adult and kids alike. So even though there is a law in most states requiring a bell it hasn't gotten to the federal level as reflectors have. And I haven't heard f any state ticketing adult riders without a bell on, in fact I haven't even heard of that happening with reflectors that most adult riders remove after purchase. There may some local towns that for the sake of needing money might be that anal but as a whole ticketing isn't happening.
HOWEVER, a word of warning, at least this is happening where I live. If you are involved in and accident with a motorist and it's technically not your fault, but it's deemed due to conditions at the time of the crash that you were riding without the required safety stuff, which is the reflectors stuff because it mandatory on bikes, that riding without reflectors may have been a contributing factor in the crash you may lose any case you might try to press against the motorist. Regardless of the word of warning most of my bikes do not have reflectors, I do have shoes with built in reflectors but that won't count because it's not considered part of the bike equipment.