I guess I was naive to think that steel would drink up solder like a copper pipe joint, but I have not been able to even get anything to stick.

I've seen "Comet" flux mentioned, where can I get some? I've tried several different flux/solder combinations and I can never get the solder to tin on steel, it just beads up and falls off.

Any other flux recommendations out there? What else might I be doing wrong?

Brownells carries Comet flux.

If it is "beading" up, I suspect you are not getting everything hot enough. Also remember to keep everything as clean as possible, it does not take much oil to prevent solder from sticking for example.

AND, if you heat it TOO hot then soft solder will never stick. That's the problem I have (too hot), so I normally use the low-temp silver-solder sold by Brownell's. The temp-limitation is one of the main reasons that the old-time solderers use(d) the big-ended copper heat sinks, they could reach the proper temp without exceeding it.
Regards, Joe

Proper prep is the key along with proper heat.

The metals have to be very clean the proper flux used for the solder being use.

Always use the larger part to transfer the heat to the smaller part.

Too many apply heat to both, the smaller part then heats up to fast melting the solder before the larger part is hot enough to hold.

You mentioned the metal soaking up the solder. That does not happen the solder bonds to the out side of both items. Then bond togather to hold the items togather.