How long is too long to wait for the best doctor?

My mom's recent biopsy diagnosis result was cancer positive: "Invasive Ductal Carinoma, Histologic Grade 2/3, Nuclear Grade 2/3 by Bloom-Richardson system."

Her primary doctor referred her to one of the best Korean doctors at the best Korean surgery hospital. For her initial exam on 2/14, the doctor examined her breast for brief 10 minutes and mentioned that the lump felt bigger than 2cm (her primary doctor noted 1.75 cm so could have been swelling from biopsy) and that she may have to undergo chemo first.

Then, we were led to make additional appointments for blood test/ct scan the day of, ultrasound 5 days later, and meet with doctor 16 days later on 3/2. They were also able to schedule us for bone scan 3 weeks later and MRI screening 7 weeks later on 4/4. We were also told that it takes about 9 weeks to make surgery appointment with the doctor we saw as he is the best of best at the hospital. So, if he gives us the recommendation to either go through chemo or surgery first on 3/2, then we are looking at about 11 weeks out from when we first met with the doctor for the initial exam to begin the cancer treatment.

All this waiting is making me really anxious and afraid that the cancerous cells are going to (or may have already) spread to other places.

How long is too long to wait for this doctor?

Should we be looking at other doctors at reputable hospitals but that are second tier hospitals who may be available sooner?

Also, I read that to figure out whether a cancer is metastatic we would need to scan the bone first thing?

I am not sure why we have the doctor appointment before our bone scan. Everything in this hospital takes a long time of waiting. I am aware of the high survival / surgery success rate but not sure if this is worth all the waiting. Please advise!!