interesting - we've been discussing hermaphroditism at uni this week (part of reproduction module, we're not that weird!)
Is "she" externally male or female? Most commonly, animals have female external genitalia, and then either a rudimentary reproductive tract internally with very small organs and no or very small gonads which cannot be distinguished as ovaries or testes, OR they are pseudohermaphrodite where they have some sort of uterus (may be small, odd shape, etc) but testes of a suitable size to the uterus, in the normal location of ovaries.
The first type usually dont ever reach puberty and so dont display sexual behaviour and characterstics of either sex. they still need neutering though as the abnormal tissues can still cause issues, especially cancers. The second type can develop sexual characteristics of either or both sexes! or neither. The 'testes' do produce hormones, so you may get male behaviours from testosterone, but they may also produce female hormones instead/as well so might be nesty, stroppy madam types. Obviously these also need neutering and the risk of hormone-related issues are higher in these animals.
In terms of bonding, i think it slightly depends on which type of hermaphrodite they are, but in theory if the hormones settle down adequately then you may have equal chance with either sex. But if they've been displaying characteristics of one sex more than the other, then probably an opposite sex bonding is more likley to work, simply because the learnt behaviours will correspond better.