I have played a lot of support in all divisions between bronze and platinum and although your question might seem simple, it's actually extremely complicated. Why?
Your decisions as a support, very often, will propel you into the mid game. The first huge objective that appears in a game of Summoner's Rift is the dragon. It is worth a lot of gold. The more quickly you can kill the dragon, the more times it will spawn, the more you can make use of the gold that flows on the map. Gold means items, means power. Every decision that you make as a support, down to the item you buy when you're first starting a game, should be intentional.
When can it be good to roam as a support?
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If you and your ADC have pushed the enemy to their tower and you force them to return to base, sometimes it's much better not to attack the tower. The tower will kill the enemy's minions, and that's gold that they will lose. The faster you kill their tower, the safer it becomes for them to farm by freezing the lane. If your ADC has enough gold to purchase an item but you are not ready to go to base, don't stick to the ADC like glue. It's useless. Roam mid and try to make a play. Or, even if you don't make a play, place some wards along the way. If you're a good support, you usually have a pink ward or a red trinket. Use it. Scan for vision. When your ADC comes back to the lane, resume as normal. But don't ever go top unless you are 100% certain you can get a kill (usually you are never 100% certain).
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If you are in an unfavorable lane matchup (you're supporting a Vayne or Twitch into a Cait that knows how to play Cait), you might find yourself in a situation where you are pushed out of lane and lose your tower early. This is okay: your ADC scales into the late game, so just let them farm. They should freeze the lane and play safe. It is your lane's job to make sure that your loss of map vision from the downed tower is compensated for. You should first attempt to keep the enemy from pushing into your jungle with wards by placing pinks and purchasing a red trinket (you should get a red trinket as soon as you purchase a sightstone). Keep the dragon warded. If the enemy decides to push bot as a duo, stay bot. You should otherwise naturally gravitate towards mid and try to make a play. Making plays wins games.
When is it not good to roam as a support?
- When in doubt, stay with your ADC--especially if you are owning. If you and your ADC are so fed that you can 2v3 enemy threats in the bottom lane, just stay together. Use the momentum of your synergy to invade the enemy's jungle with wards. Place pinks, defend them, and push to the next tower. Always control the dragon, at least early. Apply your own pressure so that the enemy team is forced to draw back from lanes they are winning to help their severely losing lane.
TL;DR - The support role is extremely nuanced. The decision to stay with your ADC or roam changes with every game.