No such thing exist in Singapore to invest in the local bourse.
First of all, who said anything about "the local bourse"? Singapore is
tiny. It would violate every reasonable, rational portfolio diversification principle to invest only or predominantly in Singapore headquartered companies, especially with CPF in the picture. SGX realizes that, too, which is why the "local bourse" offers lots of non-local ETFs. You can and should seek low total costs, consistent with reasonable investment objectives.
You can't invest in local shares using IB.
Who said anything about IB specifically?
However, as it happens, yes you can! Symbol 3065, traded on the Hong Kong Exchange, is one way to do that. Symbol EWS, traded on the New York Stock Exchange, is another. Those two are pure play Singapore ETFs, investing only in Singapore listed/headquartered companies. They're exactly analogous to STI-based stock index funds traded on the SGX. I don't recommend either ETF, but they exist.
What I do recommend, if you want ample exposure to Singapore (and
some exposure is appropriate, I think), is to consider a more diversified fund as part of your portfolio -- an ASEAN-oriented ETF, for example. There are several such options traded on various exchanges, locally and overseas. ASEAN-oriented ETFs have a lot of Singapore in them, but they don't
only have Singapore. One "reasonable" approach if you want to overweight Singapore would be to combine an ASEAN-oriented ETF with a global developed markets-oriented ETF. Always with low total costs in mind.
Rewinding a bit, all I said is "low cost broker." I didn't specify whether that broker is in Singapore or elsewhere, and I didn't recommend any particular funds, equities, or other investment vehicles. But, now that you ask, I suggest looking for the best deals worldwide, consistent with reasonable, rational investment objective principles, notably portfolio diversification.