High, is there a way to use aliases, which I have defined in my local ~/.bashrc ? Thing is I have there pretty shortcuts for some programs with awful lot of parameters and do not want to start bash every time I want to use them
Do you know of some way, how to accomplish it?

Unfortunately, KRunner is not aware in any way of bash aliases, it is only aware of actual system commands. To be aware of them, it would essentially have to implement parts of a bash interpreter, which would be quite resource intensive and bug prone.