Electric mats are for directly under tile, you won't have enough heat to retrofit. You might try a really high level of insulation.

I can't begin to understand what you deal with in Minn but anything you can do to raise the temp of the basement might help. The fact is that tile will always feel cold without supplemental heat but really good insulation will help.

hydronic can be done (for a small area) off a hot water tank.
Your water heater.
It can be done.
It is done.
North of you, in Canada, with the same codes (same electrical and plumbing) for all intents and purposes, in Edmonton and Calgary.
Look to Canadians for "spot warming" advice.

david_cary is usually right but here is a case where I'll rewrite the concepts a bit.
1./ insulation is only good if you have a heat source, so insulating underneath the tiled floor is only good if there is a heat source between the tiled floor and the new insulation. Without any new heat source, any and all new insulation will only serve to keep the tiles warm IF you laid down on them for hours and warmed them up. Otherwise new insulation will be pointless, and will frustrate you.
2./ basement warming will not end up in the bathroom floor tiles, for all practical purposes, unless you overkill the concept of basement warming. If this needs more explanation I could write a few sentences more.

Hope this helps.

"insulation is only good if you have a heat source..."

Disagree. Insulation helps maintain a steady state.
Not that I disagree with your assessment.

"Could standard electric underfloor mats be attached between floor joists from basement...?

Short answer, yes. But of course, effectiveness depends on actual construction and materials. Do you have ceramic tile on bedboard on wood subfloor? Iffy.

Any heat you put under the floor will radiate into adjacent material(s), doesn't matter whether water or electric is the transfer medium. If it wasn't for kWH price and demand, electric would be hard to beat.

You would have a substantial lag between start time and comfort with an aggregate of poor radiating materials.

All the above cast doubt on 500 bucks. But thirty sq.ft. isn't a lot of area either.

I did get an estimate for the hydronic heat from water heater--over $2000! so that is out--darn it. That would be my first choice, but too expensive. Maybe I should get more estimates?

Yes, floor is ceramic tile on cement board (or whatever they use) on wood subfloor. House was built 1927, if that makes a difference. Walls are also tiled.

""insulation is only good if you have a heat source..."

Disagree. Insulation helps maintain a steady state. "

Insulation only slows the movement of heat, it does not produce heat or stop the movement.

Without some source of heat all that you will have is an even colder room.
The insulation also prevents heat from moving INTO the room from a warmer area.

brickeyee, this is the best so far. The best way to word it. The other two statements were both good but not quite, because they could be refuted with a little effort. Yours is best because it is short, simple and hard-to-refute.

".... good but not quite, because they could be refuted with a little effort."

Oh? Refute "helps maintain a steady state" please.

it would be easy to maintain the position that those words were appropriate and sufficient.
so, any arguing the opposite point of view might end up in a zero sum exercise.

the thing brickeyee did was to make it more practical to the end user who has to run with the knowledge obtained.

the mental model is slightly altered when one introduces the notion of heat source.

ta da.
hope you are open minded enough to let it be.

--

one thing I wrote wrong in my first post was not saying the heat source could be above the tiles (or below); any heat applied to the tiles.

Just curious about your using "refute", as in to prove false, since it is not my intent to misinform.

Thermal insulation inherently means seperating one temperature from another, thus intending a steady state, whether subject to "heat source" or "cold source".

Exploring clearer language hopefully does not imply closed mindedness.

to refine it a bit, rebut might be finer than refute.

steady state is the concept that is most rebuttable since insulation slows down heat transfer so it only gives one the impression of a steady state; it does not truly maintain steady state, since it allows heat transfer to occur. (Everything allows heat transfer to occur and nothing stops it).

OK, gotchya.

Why I said "HELPS maintain a steady state" not

MAINTAINS a steady state.

"Everything allows heat transfer to occur and nothing stops it"

Yes, but since most of us prefer a steady state, insulation is usually better than none at maintaining it.

I know you do not want to pull the tile but before you walk away totally from that idea take a good look at what you have now and go browse through some tile. I am in MO and know how much cold tile stinks and don't want to imagine MN. You might decide it is time to change the look and add some mats so you have the new look and warm to boot. IMO this would be your most cost effective alternative.

with or without insulation, in the bathrooms forum, this topic is often discussed.

Here is a link that might be useful: To heat or not to heat the floor? Help me answer the question