wow...total fail at no radiator cap???
Yes, make sure the heater core is being allowed to flow(vent to the hot setting, but keep the blowers off...no need).
I just burped the old Civic. Got a UOA on the road, worried of internal coolant leak. Best 'worst case' would be water pump gasket is leaking. It happened on the first road trip I took the Civic on. About 1,750 miles or so round trip.
The destination...okay coolant level was down some but still visible at the radiator cap. Added some to the radiator and some to the overflow tank. Total fail man...had to bleed it properly once home with my spill-free funnel kit. It let out 2 or 3 large 'gulps'.
The problem is I also appear to have a leak, probably the water pump seal losing coolant at the weep hole. Such a pain as the timing belt job was done just 20,000 miles ago...
Will be removing the VCG and inspecting things down the timing belt area with the upper cover also removed. Hopefully, all you have is air trapped. Great suggestions to park with the radiator above the rest of the cooling system, flipping the climate controls over to hot (no blower needs to be running) and seeing if that will help it self-purge.