You don't need a bleed kit at all for most bicycle hydraulic brakes. I've replaced calipers and hoses, and I never needed one. Air always tries to go up in oil, so just hold everything so that the only way is up.
You never need to replace the brake fluid either. That's a scam when they do it to your car or motorbike. They tell you that the oil can absorb moisture, but the system is completely sealed. There's nowhere for the moisture to come from unless you open the reservoir every day to check something. My motorbike was 20 years old with 40, 000 miles and never had anything done to the coolant or brake fluid. Everything worked perfectly, especially the brakes. It had only done 1100 miles when I bought it, so all servicing was done by me. All it ever needed was engine oil and filter change, brake pads, occasional light bulb, tyres and occasional lube on the choke cable.
I learn something new every day on this forum.
I remember years ago, me and my mate fitted a complete new front brake on his Suzuki GSX600 . All the components were dry and needed filling with hydraulic fluid.
We naturally assumed we'd just have to fill the reservoir, open the bleed screw on the caliper and pump it through.
But it didn't work, the fluid refused to budge no matter how much we pumped the lever.
A quick trip to our local motorbike shop and had a chat with a mechanic. He said we were filling it from the wrong end, he suggested we get a big syringe and pump the fluid into the brake from the caliper bleed hole and up into the reservoir until you got to the right level. It worked, once the brake components are filled with fluid you can bleed it to your heart's content.
Of course with pushbikes one simply buys the complete brake system pre-filled with fluid, just shove it on the bike, tighten three screws, job done.