From your description of what you do, it sounds like you interact with the paying public, so are subject to the full force of public safety, liability, elf'n'safety etc.
From a safety point of view ...
A LED bar that is specified to operate off 12v to 30v DC is probably not rated to operate at other potentials. If you connect several in series, then some will be at around mains live. I can see local authority inspectors and insurance companies coming down on you like a tonne of bricks for bodging 'low voltage' things into series and running off mains.
From an operating point of view ...
The 12-30v input spec sounds like it has electronics in it to operate from a range of voltages. That sort of range is common when the intention is to use one or two automotive batteries in series. This might, or might not, get upset if fed with rough DC, say from a simple bridge rectifier. It would certainly get upset if fed with AC. How clean the DC would need to be to operate properly, how much reservoir C on the bridge rectifier could only be guessed at.
You might want to consider a PC power supply with its 12v output. They are relatively inexpensive, and are rated to be connected to the mains safely. There is an issue over how much 5v you would have to draw to get the 12v output regulated, so maybe that's not such a good idea.
A single 24v supply for the whole lot sounds the best route. Given the wide input voltage specification of the bars, you might be able to tolerate poor voltage regulation, and possibly much ripple, so do not need one with gold-plated specifications.
Now the question is, where does the DMX relay go? Ideally on the mains side, lowest current, and where it is 'rated'. However, that needs a power supply capable of powering up quickly (and repeatedly?), you would need to check. If on the DC side, you have 60Amps at 24v, not a trivial current, so you would need a suitably rated, and rated for DC, relay.
If you already have, or have paid for, these low voltage bars, then you're stuck with finding a way to power them. If you haven't yet invested in them, you might want to see whether a mains input type is available, that you can use directly, or ones with a standard control input exist.