You aren't weird and not wanting to dance with anyone except your partner is very common. However, going to a dance party and not dancing with anyone except your partner is often considered 'unfriendly'. Also, although you might not mean to, you are putting your partner in an awkward position. Dancing has always been a social activity first and foremost. I would say yes, get out there and it will become easier. If it is too much for you and you turn women down, just be aware that some will not understand and you might come across as snobby or rude. Perhaps an explanation - "I'm sorry, I'm just not confident enough yet to dance with anyone other than my partner" - might help. No one likes to be turned down after awhile they will stop asking.