Exchanges charge their own fees in any case which Bloomberg passes on to the end client with no markup, hence they don't really care about the fact that it goes

Exchanges charge their own fees in any case which Bloomberg passes on to the end client with no markup, hence they don't really care about the fact that it goes through Bloomberg (in-fact because Bloomberg make it easy to subscribe to new exchanges Bloomberg is probably a net positive for the exchanges). Insider trading is a risk, but no-more so than with everyone else in the financial industry. If you work in finance typically there's pretty tight restrictions on what you're allowed to trade on a personal account (i.e. no shorting, no holding equities for less than 30 days, etc.) and you have to register any non-blind investments (both so things like insider trading can be tracked but also to prevent conflicts of interest).