This is related to this question.
The anatta concept doesn't say that there is no self - it says "not self" as in "all phenomena is not self". There is a self, but it is not permanent and is not independent from the inter-workings of the senses, sensation, perception, mind and consciousness.
For e.g. a static image that is projected on the wall - it is a result of light projected onto a wall from a projector. If you dig deeper, you can explain how a projector works, how electronics and electricity works. The image does not exist permanently and independently from the wall or projector or electricity. But this does not mean that the image does not exist. Surely it exists.
Also, to quote this answer, anatta relates to absolute truth, however, the self that exists relates to relative truth.
While you have not yet attained Nirvana (Bodhisattvas included), suffering is still experienced, hence the self still persists and rebirth continues to take place. When you knock your head on the wall and say "ouch", you know that you are still subject to suffering.
In the Acela Sutta, Kassapa asks the Buddha whether the suffering that one experiences, is caused by oneself, is caused by another, is caused both by oneself and another, is not caused by oneself or another but arises spontaneously, or it doesn't exist? The Buddha says that suffering exists, but it is not useful for us to speculate "who" ultimately caused it, from the perspective of absolute truth. If the self caused the suffering, then it is the eternalistic argument. If no one caused it, then it is the nihilistic argument. But instead, the Buddha taught Kassapa the middle path, which is dependent origination.
So, it is also not as easy as there is no self at all, or that there is definitely a self, and trying to link the effort to liberate oneself or other beings to one of these. Rather, the Buddha prefers us to ignore that part ("Don't say that, Kassapa") and focus on dependent origination.
Compassion by itself can be a contributor towards liberation from suffering according to the Nissaraniya Sutta:
It's impossible, there is no way that — when compassion has been
developed, pursued, handed the reins and taken as a basis, given a
grounding, steadied, consolidated, and well-undertaken as an
awareness-release — viciousness would still keep overpowering the
mind. That possibility doesn't exist, for this is the escape from
viciousness: compassion as an awareness-release.'
I don't think Theravada lacks compassion, as it teaches the practice of the Brahmaviharas. But is it selfish to liberate oneself before trying to liberate others? Well, I think in Theravada there are the four stages of enlightenment (which can last up to 7 births from the first stage), plus an Arahant can continue to teach, till parinibbana, so there is still plenty of chance for one to contribute towards the liberation of others, but not quite till the hells are empty.