From the Catholic perspective, the universal teaching is that all persons are called by God to chastity, which is understood as a successful integration, inner unity and rational expression of human sexuality, both within the person as well as in interpersonal relationships (CCC 2337).
The Church helps sinners in a variety of states of life—including those who are married, were previously married, or those who remain single or devote themselves to celibacy—by encouraging them to express chastity in different ways. Each of these is valued, including the friendships offered by and to those not in sexual relationships (CCC 2349 and 2350).
The Church does not teach that having a homosexual or bisexual tendency/orientation/attraction is itself sinful, as sin relates to choices and actions/behavior. However, all sexual acts that are not open to life—i.e., all sexual acts outside of heterosexual marriage—are understood as sinful because they are expressions of sexuality that lack one or more of the essential qualities of the type of sexual expression to which we are called as Christians. So sinful behaviors would include homosexual acts, heterosexual acts outside marriage, as well as acts that are not open to life, even when within a marital relationship. So the Church would most likely say that the bisexual person is called to chastity and to cultivate inner freedom in order to choose either celibacy or heterosexual marriage.
Above, I mentioned that celibacy and singleness are recognized as valid lifestyles, and there are many examples of Christians who are not inclined to marry, often those who remain virgins and/or enter religious life. Additionally, consider this passage of Jesus' teaching:
Matthew 19:8-12 Jesus replied, “Moses permitted you to divorce your wives because your hearts were hard. But it was not this way from the beginning. I tell you that anyone who divorces his wife, except for sexual immorality, and marries another woman commits adultery.” The disciples said to him, “If this is the situation between a husband and wife, it is better not to marry.” Jesus replied, “Not everyone can accept this word, but only those to whom it has been given. For there are eunuchs who were born that way, and there are eunuchs who have been made eunuchs by others—and there are those who choose to live like eunuchs for the sake of the kingdom of heaven. The one who can accept this should accept it.”
Please note that the word eunuch is not restricted to those who are physically castrated, but can also include those not inclined to marry, and the passage also references those who choose to live like eunuchs. So in both these examples (Scripture and the Catechism), virginal or celibate life are promoted as valid and valuable expressions of one's sexual identity, and the church does not teach that all people should seek or participate in a sexual relationship.
So according to Catholicism, both the person who experiences a deep sexual attraction to members of both sexes, as well as the person who does not experience this type of sexual attraction toward either sex have the opportunity to live out either a sinful life or a chaste and holy life, depending on the type of behavior they choose to engage in.
The church does teach that as part of being human, we all have a sexual identity (CCC 2333). It is possible that the case of someone who chooses to radically reject their own sexual identity, or the case of someone with a deeply wounded identity where the person is not able to bond or form healthy friendships might be considered problematic, but this does not appear to be what you are describing, and this would not likely be described as sinful.
The CCC references I've included are to the Catechism of the Catholic Church. If you are interested in learning more about what the church teaches about chastity and the nature of human sexuality, I'd recommend reading the first two sections of Article 6. You can easily search for these references online, or follow the links. Both sections together are only a few pages long.