It's not uncommon for judges to set bail at an amount so high that a defendant can't afford it, even through a bail bond company. Rules vary from state to state and from state to federal court, but defendants are usually entitled to some form of bail review, whether through an appeal or a petition for writ of habeas corpus.
(For information on bail while appealing a conviction, see Bail While Awaiting Appeal.)
In order to appeal a ruling, it must be final. In some states, bail orders are considered final, meaning that defendants can appeal the amount of bail or denial of bail. In other states, a bail order is considered interlocutory, essentially meaning that it’s intermediate or subject to change. Since an order typically has to be final before a defendant can appeal it, most interlocutory orders can’t be appealed. But in some states there’s an exception that allows defendants to appeal bail even though bail rulings are considered interlocutory.
In states where defendants can’t appeal bail rulings, they can usually use a petition for writ of habeas corpus to challenge the judge’s order.