An at-fault will affect your car insurance if it happened in your car. Depending on who you're insured with, it may or may not affect your bike insurance.
My accident 5 years ago basically restricted me from getting a car but my bike insurance stayed low.
Most insurance companies offered me between $350-$400/mo for an entry level car while my bike insurance gradually decreased over the years due to "experience" and age starting at $1950 for a cbr125 (1M Liability + Fire and theft at the age of 19) to $1100 for 1M full coverage for a ninja 300 for a ninja 300 at the age of 23.
RBC Insurance and TDMM did not increase my bike insurance from the accident (Spoke with insurance agents) while Statefarm seemed to have an increased a bit from the accident.
Edit: The year after I got into my accident, my insurance quotes were around $600+/mo for an entry-level car. But keep in mind I was around 18-19 years old at the time.