Usually I just cross districts like this and move further to my destination. Purvciems is separated from Bikernieki forest by several streets and so it`s not connected with forest directly.
However, many of forests surrounding Riga and in Riga itself, are very nice - pine trees, sand dunes, small lakes. Also garbage in some places. Thankfully, there are some ongoing activities, like project "Pēdas" FOOTPRINTS, to make these places cleaner.