I'm not a gambler, but it's probably doable:
It depends what sort of payments your chosen gambling site accepts. If they accept bitcoins, then simply buy some BTC at an exchange funded using your bank account, then withdraw your new BTC from the exchange directly into your gambling account.
If you chosen gambling site doesn't accept BTC, you could always still transfer it via and exchange, although this seems a bit silly as there are probably cheaper services to send the money via.
With this method, you'll obviously incur transaction fees at the exchange, as well as deposit/withdrawal fees, and possibly currency conversion fees.
Another alternative that wouldn't use Bitcoin would be to send the money via TransferWise. TransferWise recently stopped handling Bitcoin related transactions, they also may not be happy about sending money to gambling websites, although I'm not sure.
tl;dr Yes - convert it to Bitcoin and back into fiat if that's all your gambling site accepts. Could prove costly though.
2Legally, I think it's pretty much dependent on what these “third parties” are allowed to do. Technically it's possible as far as you can use a bitcoin exchange from your bank account. What kind of answer are you expecting from the bitcoin community? Could you clarify your question? – Stéphane Gimenez – 2013-09-18T13:44:37.297
1The technical possibility obviously is available, as the bitcoin gambling space is thriving and there are numerous websites that accept payments in bitcoin. If that is what you are asking, the question shows 'no research effort'. However, if this a question concerning the legality of setting up such a service in Norway, you should consult a lawyer in Norway. :) – Murch – 2013-09-18T14:39:11.600
why not just gamble with bitcoins. More easily verifiable and fairness will attract customers – CQM – 2014-04-11T16:00:10.153