yOU CAN subcukture bacteria in a)Peptone water and b)Peptone water containing the polkant extract, amd the subculture 1 llopful from both on blood agar and egg yolk agar. You can look for inhibition of hemolysis, loss of lecithinase, lipase , protease etc, if present. You can also do Gram stain from both suspensions, to see if Gram satining pattern is changed, e.g. a Gram positive organism becomes gram negative.this will indicate damage to cell wall. Test tube method van be used to see if biofilm formation is inhibited.
You can check your extract and antibiotics in the following assays i.e Fraction inhibitory concentration and Time kill assay. It will be helpful for your question.
Mostly plant extract is a complex mixtures. First we have to know the classical structure and quantity of major component present in extract. Then we can interpret the same by applying biochemical method as in Antibiotics.