With improving performances for both club and country, Bulykin, who had never hidden his desire to move to a foreign club, was expected to move abroad. In January 2004 he spent two weeks on trial with Everton, but he did not have enough caps for a work permit. In 2005, hoping move to England, Bulykin went on trials in Portsmouth but that transfer did not happen. As a result, Bulykin remained with Dynamo, and was quickly relegated to play in the second team, and eventually excluded from training process altogether.