If you're very motivated, it may work.
If you can obtain handcuffs, then you likely could obtain asphyxiant gases as well. Displacing oxygen from the bag and breathing with oxygen-deficient atmosphere should render unconsciousness quickly.
It's enough to reduce the concentration of O2 to 6% (that is approximately 28% air + 72% simple asphyxiant) or below to induce LOC within a minute. The 3rd stage of general anesthesia (sufficient for surgical operations) is achieved within ~3 minutes (the actual time may be much smaller).
Nitrous oxide is one of the best asphyxiating agents, since it has a light sweet odor, produces anesthesia slightly faster than inert gases (like nitrogen), and may suppress the symptoms of dispnea caused by excess of CO2 according to the studies described in the documents below
It's widely available in online markets as food additive E942 used for making whipped cream. A cheapest package of 10 x 8 g N2O chargers costs nearly $5, and 8 g of liquid N2O expands to ~4 liters of gas at atmospheric pressure. A cheap dispenser (that would be handy for cracking the chargers) costs nearly $15 - $25. This is far less expensive than typical recommended open/ventilated inert gas setups.
Making a well working unventilated setup requires some good dexterity though, since allowing too much air entering the bag could result in some complications.
It was found that anaesthesia can be obtained with mixtures of nitrous oxide and air, provided the latter does not exceed 30 per cent. With 33⅓ per cent Hewitt failed to induce complete unconsciousness. With small percentages of air the symptoms were practically identical with those produced by the pure gas. The greater the proportion of air, the longer was the inhalation period before symptoms of anaesthesia appeared. Thus with 3 per cent and 5 per cent of air the average inhalation period was 69 secs.; with 30 per cent of air it was 148 secs.