Most of the schools in the Eastern Collegiate Cycling Conference receive some funds from their school, roughly a few thousand dollars on average.
Consider what resources your school may offer your team besides cash, either for free or at a reduced cost:
Use of school vehicles (or arrangements with vehicle rental companies for discounted rates and/or permission for drivers under 25 to operate rental vehicles)
Free gas at school pumps, or free/discounted gas via gas cards
Discounted apparel through official manufacturers
Most teams require members to contribute dues to be part of the team, often with additional benefits (such as a free jersey, or free race entries). Dues range widely between teams, typically in the range of $50-$250. Consider the financial gain from dues, opposed to the barrier to entry that may turn away potential members.
You may also offer that new members can come with the team to their first race without paying dues, and may want to have "tiers" of dues, for instance letting members who don't participate in multiple seasons pay less.