I worked on a convert desk at a Ibank I know what I'm saying.
yes anyone can buy and sell them just like corp bonds. trouble is they are less liquid, and get allocated very quickly at issues. not every dick n harry can come along and take a 50mm issue at a good bid, so you gotta know the MMs. like private equity placements and private notes, relationships and who u know matter in this business.
converts are difficult to price, so everyone has their own pricing model. they are not as simple as a corp bond + options. they behave like corp bonds deep out the money, and more like equity close to in the money on the option part.
find yourself a broker that deals with them if you want access to trade. but you'll find you're going no where unless you're dealing with names like JPMorgan. small brokers, intermediats may have some inventory but also crap prices to trade of.
heard of ASCOTS? theyr stripped converts. you retain the equity optionality and get rid of the corp bond element. you got a cheap option and can remain short delta.
apply for a prime brokerage account with JPM, Goldman, Deutsche or someone of that calibre if you're serious. otherwise get a clerk job on a convert desk in a bank and then get on the trading desk.
this is like a retail equity trader wanting to trade CDOs. you won't without the right money.