* Alenka Bratusek resigned after losing party leadership
* Opinion poll puts her in second place if she forms party
* Markets want her economic rescue plan implemented
* Slovenia narrowly dodged bailout, risks remain
LJUBLJANA, May 9 (Reuters) - Slovenia's outgoing prime minister Alenka Bratusek has a fighting chance of doing well enough in a snap election to allow her to return to power and implement the economic rescue plan that markets believe is needed to stave off a bailout.
A euro zone member, Slovenia narrowly avoided an international bailout last year and has committed to selling off state assets to cut its deficit, but that plan was upset when Bratusek resigned after losing the leadership of her party.
A comeback by Bratusek - a 44-year-old former finance ministry official who had been seen by markets as a guarantor of political stability and fiscal responsibility - would be remarkable because as yet she does not even have a party.
But signs already point to a major post-election role for Bratusek: 14 of the 90 members of parliament have already joined her, an opinion poll forecast that if she forms a party it will come a close second in the election, while her more established rivals are tainted by corruption allegations.
"Public support for Bratusek is rising because she has managed to distance herself from the political establishment," said Grega Repovz, chief editor at Mladina weekly.
Bond yields rose after Bratusek's defeat in the battle for the party leadership but have since fallen gradually as the markets embraced the idea of an early election.
Much remains uncertain because a date for an early parliamentary election has not been set, and the parliament that results is likely to be fragmented, leading to protracted negotiations on forming a coalition government.
Also, the election could favour left-leaning groups who, if they emerge from the vote with enough support, could try to water down the privatisation plan that Bratusek set in motion during her 13 months in power.
The biggest risk facing Slovenia is that market jitters about political instability will force up the cost of borrowing. That in turn could make it impossible for the southeast European state to turn over its debt, forcing it to seek a bailout.
However, Slovenia has already covered its financial needs for this year by issuing four bonds in the joint value of some 4.5 billion euros earlier in 2014. They should also suffice to at least partly cover the repayment of debt in the value of 1.2 billion euros that will mature next year.
The yield on Slovenia's 10-year benchmark bond eased to 3.441 percent on Friday versus 3.465 percent a day before, according to Reuters data.
MARKET WANTS QUICK VOTE
Bratusek resigned on Monday after losing a contest for the leadership of her Positive Slovenia (PS) party. Her government will stay on until a replacement is formed.
The parties in parliament have agreed that there will be a new election, instead of trying to cobble together a new coalition from the existing parliament. They are to decide in coming weeks if the election will be held in July or September.
"Privatisations that have already been started will not stop but the caretaker government cannot start any additional reforms so it would be market-friendly to hold an election as soon as possible," said Primoz Cencelj of investment firm KD Skladi.
An April 29 opinion poll commissioned by broadcaster Pop TV put the centre-right SDS party on top with 13.4 percent support, followed by Bratusek's as-yet-unformed party on 12.2 percent.
The centre-left Social Democrats, who are uncomfortable with the sell-offs, were in third place with 9.4 percent.
Positive Slovenia, under new leader Zoran Jankovic, had 5.5 percent, according to the poll, the only one conducted so far which included a future Bratusek party. A new group, Verjamen, had 4.5 percent. Its policies are unknown but it is likely to appeal to left-leaning voters who dislike privatisations.
Seventeen percent voters were undecided while 16.6 percent did not plan to cast a ballot.
Bratusek told Reuters in an interview this week that she may form a new party. Already, some 14 legislators have left Positive Slovenia and joined an informal grouping loyal to her.
Her prospects are helped by corruption cases against two of Slovenia's biggest political heavyweights - Jankovic, who is also mayor of the capital Ljubljana - and two-time ex-prime minister and current SDS party chief Janez Jansa - that could dent their ability to form a coalition. Both deny wrongdoing.
(Editing by Christian Lowe/Mark Heinrich)