I) For a newbie, coming up with significant (or even modest) bounty is difficult.
II) A newbie is more likely to feel more "stuck"/"helpless" in some situations than a "pro", but it is the pros who can comfortably use bounties.
III) A newbie need not be a newbie in all fields. For example's sake, someone may be an algorithm expert, but can do with some help as a webmaster.
Keeping in mind the above, here are few suggestions that can make the bounty system more useful (all suggestions can be improved, but just conveying the points):
1) Cross-site bounties: Example: allow users to use their reputation on SO as bounty on superuser, etc.
2) Allow 'special' reputation points: A newbie is given say 200 reputation points which can only be used as bounties. No powers associated, and not counted/displayed as actual reputation.
3) (I don't particularly find this elegant): Allow a 'credit'/'debit' system. Allow people with low reputation to effectively go negative for some time, should they need to throw a bounty for something important to them.
All said, maybe bounties are rarely used, and maybe, the SO team wants to encourage only experts to raise bounties (for a valid reason). But from one point of view, the newbies can do with ability to throw more bounties.