The drip system should really be attached to a water meter at the spigot. The water meter will tell you how many gallons are flowing through the hose over an interval of time. You can then use this number and divide it by the number of roses you have, and determine how much water each rose is getting in that same interval of time. You can then use this information to calculate how long to leave the hose on, in order to dispense whatever portion of a gallon per rose you desire. In other words, it's as much a function of flow as it is time, and water pressure can be a determinant, too.
But unless or until a meter is installed, there are some other work-arounds you can use to know how much water you're putting out per rose, depending on what type of drip system you have. There are several different types of systems that come to mind:
One type that I've used has a long, hard plastic tube to which individual thinner tubes are attached through puncture holes, and those thinner tubes are routed to individual plants. Those thinner tubes have tiny little shower heads at the end of them called dribblers or emitters. Each dribbler can be adjusted for how much or how little water it lets out. If you have a dribbler system, you can place one of the dribblers into a gallon milk jug or bucket or other container. Let's say you want to give each rose a gallon of water... then you just wait until the gallon container is full and then turn the system off. Or you note the time it took to fill the gallon container, and multiply that by the number of gallons you wish to put down.
Another type of watering system is known as an "in-line drip" system. It uses connectors between sections of plastic tubing that allow water to drip out as it flows through. If this is what you have, you can place a disposable aluminum tin pan like you use to roast meat in the oven, and place it beneath one of the drippers. Let's say you want to put down about an inch of water around your roses. Just keep an eye on the tin pan and wait until it has an inch of water in it, and then turn off the system. Or you can note the time it took to fill the pan with an inch of water, and multiply that by the number of inches of water you wish to dispense.
A different type of drip system is a "soaker" hose made of porous or permeable material that allows water to seep through the hose into the soil beneath it. The hose can be snaked around plants, or placed along a straight line to water a rose hedge, for example. An aluminum pan as suggested above can be used with soaker hoses to capture and measure the amount of water dispensed.
If you have some other type of system, perhaps the above ideas can be adapted to how your tubing works. Just figure out a way to capture and measure the amount of water the system puts out per rose during some interval of time, and run your calculations to determine how long to leave the system on. I hope this is useful information. It's nice to know you're helping out in a public garden with such care and consideration.
