Is there a way to fill your tires with nitrogen?

There is and I have done it with the same setup. I am a diver by trade and I experimented with the same setup. I used a SCUBA bottle and set the regulators with my calibration equipment. I got it to work but it the only value I got from it was knowing that it could be done. The N₂ was expensive, at least compared to air. The SCUBA regulators were expensive and they needed to be precisely set. Calibration is usually not accurate to 1PSI, which you would need. I also didn't want to haul the whole heavy potentially dangerous HP gas setup around with me.

I dove with He on several occasions. That is even more of a hassle. The whole system would leak no matter what. It was because the Helium molecules are so small they can pass through cracks of pipe fittings no matter how tight the fittings were.

I can inflate my car tires to proper pressure by checking them once a month or so and inflating them as needed using free air. It takes me maybe 5 minutes per month.

I can inflate my bike tires to proper pressure by checking them once a week or so and inflating them as needed using free air. It takes me maybe 2 minutes per week.

There is no strategy of using alternative gasses that can even remotely compete with that in terms of economy, time or convenience.

I am going to be presumptuous enough to ask what I believe is the question behind the OPs question, then answer that...

The problem is that you have to inflate the tires more often than you like. The question then is what can I do to ensure my tires remain inflated for as long as possible.

The answers Tubes - these keep the air molecules in. Thicker is better, as is better material. Dump the super thin light weight race tubes and get the thickest one you can find, I would even suggest giving cheap chain store tubes ago.

Tires - Bigger tires can carry the same weight at lower pressures. Put in bigger tires and run at lower pressure. This has two effects - lower pressure leaks molecules slower, and more volume means those leaked molecules are noticed less.

Exotics Look at the no-tubes and 'no puncture' slime solutions - these seal the holes the air molecules are escaping from.

As previously suggested - invest in a decent pump. If you don't have room or desire for a floor pump by the door, get a pump that uses CO canisters (and wear the cost of canisters). If it is still a pain to pump up your tires - discard the plastic valve caps, and get rims/tubes with presta valves - it will take less than 30 seconds to top up two tires.

You might have guessed all these solutions add weight and move away from the best of the best in terms of performance- well, that is expected, nothing is free and super light weight fast racing tires leak air, after all, as long as they stay inflated for the stage - up to 8 Hours, that's all that is needed and any longer is excess weight.

If you have nitrogen inflated car tires then you can syphon (a little) nitrogen off of them into your bike tires. Of course, you'll have to later refill the car tires with nitrogen. (You could even overfill your car's tires at CostCo to help with this.)

Get a Schrader barb at a hardware store. Cut the hose off a Presta/Schrader bike pump and attach the Schrader barb to the cut end. Attach the Schrader end to the car tire and the other end to your bike tire.

This will only work to equalize the pressure between the two, to say 45 psi or whatever your car's tire pressure is. So you'll need something like wide tubeless bicycle tires which are good for such low pressures.