Building a relationship with a Buddhist can be tricky. First we need to respectful of there beliefs and what they hold to be true. Most Buddhist come from an Asian background with different culture and values. We should not scoff at them and have a superior attitude. Also we should actively listen and understand where there coming from. We want them to be open and receptive to us and not emotionally shutdown. By doing some of these steps they will be more open to hearing my message and truth.
One barrier that can exist is that Buddhist believe that the only way to reach enlightenment or nirvana is by following the middle path. They believe in many paths to reach God. There is no heaven for a Buddhist. Once nirvana is reach there is nothingness. Which means the person is responsible for the way they act towards others. They want no bad karma. A Buddhist view sin as a illusion and that desire is misinterpreted as evil. Also some Buddhist might look at Jesus as just another spiritual teacher the way that Buddha was.
Some personal challenges that may arise is that Buddhists deny a intimate relationship with any type of god. By showing a Buddhist how you can find love and peace through knowing God may help to overcome that challenge. Another obstacle can be a Buddhist believing that to desire is to suffer. By showing them that it has to be the correct desire and that getting rid of all desire is next to impossible would be a good message to relate to a Buddhist and point to Matthew 5:6 to further justify the truth