Try Charles Schwab
Another option is Charles Schwab, the U.S.-based broker. Charles Schwab has a Singapore-based account at Citibank Singapore for receiving Singapore dollar funds from your Singapore bank account into your U.S. dollar-denominated
Schwab One account. Fund transfer instructions (e.g. via local Singapore GIRO) are available
here. You must be sending your own funds from your own account (in your name) to your own Schwab One account, also in your name. The currency conversion spread is typically less than 0.25% above the hypothetical frictionless mid-point between currencies, which is rather good really.
There are no inactivity fees and no transfer fees with a Schwab One account. In fact, you can get a Schwab Visa ATM/debit card to tap into your U.S. dollar funds. (Schwab even rebates ATM fees, so it's actually less expensive to transfer Singapore dollars into your Schwab account and use your Schwab ATM card anywhere outside Singapore than it is to use your Singapore-issued ATM card outside Singapore.) If you want to buy stocks, options, ETFs, etc. then Schwab has very reasonable trading fees, typically US$8.95 per trade.
Funds held in a Schwab One account are SIPC insured (to a limit) but not necessarily FDIC insured. (FDIC insurance is stronger.) Also, interest paid on the account is not particularly generous. Consequently I wouldn't recommend keeping too high a balance in the main account. However, I believe you have some options to move cash into the equivalent of fixed deposits if you want to earn a bit more interest. Note that if you are not a U.S. resident or U.S. citizen you'll fill out a W-8BEN form and be subject to 30% withholding on interest, dividends, etc.
If you want to support some U.S. (and even global) spending Schwab is a good vehicle. If you've got a particularly generous rebate on a Singapore-issued credit card that can overcome its higher currency conversion fees -- a promotional rebate offer -- great, use that card for that specific type of spending on that occasion. If you need to rent a car, use your credit card, but you don't actually have to pay for the rental car using a credit card. You can settle the bill at the end of the rental using your Schwab Visa debit card. (Just tell the agent processing your rental car return that you want to change the payment card. No problem.) In general your Schwab Visa debit card (and occasional ATM cash withdrawals) would be a good, lower cost way to spend money outside Singapore.
I recommend dollar cost averaging as you convert funds. That is, let's suppose you want to build up a balance of about US$10,000 in your Schwab One account over the next 6 months, and let's suppose today's exchange rate is 1.35. That's about S$13,500. Round it up to S$14,000, and divide by 6, and you get about S$2333. Transfer that amount every month for 6 months on a scheduled basis. (Most banks in Singapore let you set up a 6 month schedule of GIRO payments using online banking.) With that program you'll tend to buy more U.S. dollars when they're cheaper (in Singapore dollar terms) and fewer when they're more expensive, but you'll end up with about US$10,000 in your Schwab One account.