We need to know exactly WHAT Russian sniper rifle this is.
Is it a Dragunov? (In reality a DMR, not exactly a "Sniper Rifle" by western standards)
Is it a WWII or earlier Mosin Nagant with PU scope?
Is it a VSS Vintorez?
Is it a
Because if it's magazine fed, you don't slip individual cartridges directly into the rifle at all, you load a fresh magazine. If it's a bolt action, it may be fed by a stripper clip, or individually topped off.
What rifle it is would add credence to the writing. Is it an old Mosin Nagant, if the character is not .gov, and not some high-speed/low-drag paramilitary type, or affiliated with law enforcement, it would be reasonable the character may have one. They're old, relatively inexpensive, millions were made, and it's more likely someone would have one stashed away somewhere, especially in non-US countries where RKBA isn't respected or as pervasive.
She does not need to get overly slavish to the details to "get it right". "She pushed a fresh cartridge into the ancient Mosin Nagant sniper rifle's magazine and closed the bolt, chambering a round"
"She inserted a fresh magazine into the suppressed VSS Vintorez sniper rifle, and cycled the action."