How does raising interest rates calm inflation?
If a central bank increases the overnight interest rate, longer term interest rates of government bonds might also rise. The longer term rate of government bonds can approximate the expectation of a series of short term rates. Everybody has a different series in mind so long term rates might decrease rather than increase.
If a private bank can earn risk free by investing overnight or longer term at attractive (higher) rates then they will invest less in individuals and businesses seeking to borrow to consume and purchase investment goods (like equipment and structures and software). If less is consumed and fewer investment goods are purchased then the rate of inflation will be lower.
An asset bubble in gold or Bitcoin is not likely to cause inflation because they are not major inputs in production. There is gold plate in electronics but not all connectors are gold plated. The ones that are not gold seem to work okay.
If oil production is constrained by a cartel, I do not know if that can be called an asset bubble but it can cause inflation.
An asset bubble in real estate can lead to higher rents which is inflationary. Since rents might have been contracted for a year or more the effect on inflation might be attenuated. Since governments often regulate housing rent the effect on inflation might be attenuated. The effect on rent is attenuated since wages change more slowly so ability to pay changes more slowly than real estate prices.
In the graph you can see inflation increased in 1999 and 2005. There was a internet and computer stock "asset bubble" and a real estate "asset bubble" in effect at those times, respectively. It seems CPI inflation can be affected by "asset bubbles". CPI without food and energy also seems to have been affected but not to a large degree. There were times in the chart when inflation was much higher than at these times. This suggests that in the current economic regime asset bubbles might not be the most important risk for inflation and asset bubbles caused by capital inflow might not be either. Perhaps these should not be considered to have been bubbles since some of these assets actually had higher prices in 2018 than in 1999 and 2005, probably even after adjusting for inflation.
However, raising interest rates also attracts capital inflows and can
create asset bubbles. Can these asset bubbles not influence the level of inflation?
I doubt that higher interest rates that attract capital inflow into a particular currency creates an asset bubble because if the higher interest rate attracts the investment, it is usually an investment into an interest yielding security or deposit. When that happens, the price goes up and the interest rate goes down and so it ceases to be an attractive interest rate.
When a currency is highly valued because of capital inflow it can attenuate inflation because imports become less expensive. The net effect of various forces on the inflation rate depends on the particulars.
If locals are a significant contributor to an asset bubble and it coincides with an economic expansion and higher inflation there might be high interest rates because of high loan demand or action by the central bank or both. If locals "believe in" the bubble then that might attract capital inflow at the same time. Outsiders might not be the main cause and they might not be the original impetus. This suggests that the cause is the inflation and the effect is the interest rates; not the other way around.