So, let's just set some ground demographics for how White Forest works in Pokemon White.
The Pokemon in White Forest are determined by the residents that are currently staying in WF. White Forest can have a maximum population of 25, however only ten residents can appear in the forest at a time, meaning ten Pokemon. The population of your forest is determined by how many days it took you to get to White Forest after starting the game. Each day subtracts 5 points from each NPC in White Forest's total points, (which is a unique value for each NPC,) and when that NPC's value reaches 0, they no longer appear in White Forest.
You do not have to reset your save file to get more NPCs in WF, but you do have to have access to copies of Black (not Black 2) that have access to Black City and the Entralink.
New NPCs can only be brought into White Forest by inviting them from Black City via the Entralink.
In order to do this, you must connect with another copy of Black via Entralink.
In Black and White (but not in Black 2 or White 2, where the bridge was removed from the game), players may choose to visit each others' worlds via the Entralink. To do that, one player must be inside the Entralink while another must be located in one of the following locations which form a hexagon surrounding the Entralink:
Black City/White Forest are two of those locations.
The visiting player would have to stand on the connecting bridges at the sides of the Entralink to make a connection and the other player's C-Gear must be on as well to establish a connection. Once connected, the visiting player would then be able to enter the other player's Entralink by crossing the barrier.
Upon entering, the visiting player would have their overworld sprite changed and appear in a black-and-white version of Unova. Everything is the same as the original, except that the visiting player cannot enter buildings or certain places, and all the routes and towns are connected via warp portals instead of connectors.
After doing this, your character in White will have to visit the Entralink of the character in Black. There, you will be able to see all of the NPCs that have left the Black City of the other game, and you will be able to invite them to your White Forest, where they will create new Pokemon for you to encounter.
If you do not have access to another copy of Black, you have to reset your save file or get a new copy of the game. I recommend playing as quickly as possible so you can get the maximum amount of NPCs in White Forest.
Tl;Dr, if you do not want to reset your save file, you need a copy of Black that has access to Black City.