What would be the general steps for making a flight in a biplane?
First follow @Jim's advice for getting the plane set up and the engine running.

A biplane is most likely a taildragger, which means that it has two main wheels and a third all the way in the back. This will give the plane a nose-high ground attitude, and taxiing to the runway will involve Scarlet to wiggle the plane left and right because the forward fuselage is obstructing her forward vision. This is not made easier by the fact that tandem two-place biplanes, the most common type, are flown from the back seat in order to get the center of gravity right.

Next, she should wait until engine temperature is high enough to run the engine at full load. I would expect that in a pursuit she skips that step but will worry that oil temperature has not reached the required temperature. The next step would be the magneto check which she will also skip.

In the takeoff run she will first orient the aircraft into the wind and then gently apply throttle so the aircraft doesn't end up in a headstand (meaning the propeller pulls the nose into the ground without the wheels moving). This also requires her to pull the stick all the way aft so the empennage (horizontal tail) keeps the tail low. A headstand is shown in the second picture of the second linked answer (this one).

Airfields back then were mostly round grassy patches, so the take-off direction could be freely selected in order to take off directly into the wind. However, you might want to add some suspense when Scarlet finds her biplane at the wrong end of the field and has no time to taxi across it, but takes off with a tailwind. This will make the takeoff run longer and the climb after takeoff more shallow, so she might just barely escape collision with an obstacle there.

When the aircraft picks up speed she should reduce back pressure on the stick and move the stick to a roughly central position in order to reduce downforce on the tail so the tail can lift off the ground. Bonus points for mentioning the gyroscopic effect from the propeller as the aircraft lifts its tail which requires the brief application of rudder to keep the nose pointed into the desired direction.

Liftoff is rather unspectacular and happens when the aircraft is fast enough. However, if elevator trim is set the wrong way, the aircraft will stay on the ground for too long (too much nose-down trim) or lift off too early at a too slow speed (too much nose-up trim). Trim means that either a spring in the elevator linkage or a small auxiliary flap is set such that it pulls the elevator to a certain deflection angle. This is helpful for adjusting control forces according to the desired flight speed and center of gravity location, but if it is set the wrong way on takeoff, Scarlet might be surprised by unusual stick forces.

While the takeoff is flown at full rich mixture, once in the air Scarlet should adjust the fuel to air mixture in the engine according to flight height. You might want to add a dramatic moment where the engine runs rough or even stutters due to too lean mixture.

After that, the escape should be easy.