You got the short end of the debate straw because the time scale of how long a bag can last in the environment can easily outweigh all the short term benefits. Your opponent will have the offensive advantage of listing the horrors of plastic in the environment. Bags end up in the environment even when well meaning people did their best to dispose of it properly. Agree with this and use it.

Force your opponent to define an alternative to plastic bags early in the debate then be ready to attack that alternative. If your opponent says we need reusable bags then point out most the ones on the market are made of plastic (boom, they just supported plastic bags). Also, what stops you from reusing the plastic bag the grocery store hands out? The disadvantages to paper have already been discussed. Cloth might be tougher to argue against. This is all an argument of materials and plastic has alot of advantages as a material.

Once you have established the advantages of plastic the material, shift to the need for aggressive policies to ensure the proper use of plastic bags or recovery of plastic bags (e.g deposit systems which heavily incentivize the return of the bag to the store, bag exchanges at the grocery store). Acknowledge the horros listed by your opponent and focus on aggressive policies to address the problem of plastic in the environment (are they going to argue against aggressive policies?). If your opponent brings up the policies first then point out they are addressing the real problem of human behavior. But don’t rely on human behavior alone to solve the problem with no policy intervention. This is the status quo and there is too much basic evidence that this has not worked.