Thanks, unfortunately, this is a client-side only mod.
 
	However, I did manage to resolve my problem using a little bit of reflection.
 
	 
	In case anyone else ever needs it, here's my solution:
 
	 
 
	@SuppressWarnings("unchecked")
	public static List<String> getBossBarNames(Minecraft minecraft) throws NoSuchFieldException, SecurityException, IllegalArgumentException, IllegalAccessException {
		
		GuiBossOverlay bossOverlay = minecraft.ingameGUI.getBossOverlay();
		String nameAfter = null;
		
		// Find the name of the field as it will change with each obfuscation of forge
		// If you're using this, you'll want to move this lookup elsewhere and store the result
		for (Field s : GuiBossOverlay.class.getDeclaredFields()) {
			
			if (s.getType().getName().equals("java.util.Map")) {
				nameAfter = s.getName();
				break;
			}
			
		}
		
		List<String> names = new ArrayList<String>();
		
		if (nameAfter != null) {
		
			Field bossField = GuiBossOverlay.class.getDeclaredField(nameAfter);
			bossField.setAccessible(true);
			
			Map<UUID, BossInfoLerping> mapBossInfos = (Map<UUID, BossInfoLerping>) bossField.get(bossOverlay);
			
			for (BossInfoLerping bIL : mapBossInfos.values())
				names.add(bIL.getName().getFormattedText());
		
		}
		
		return names;
		
	}