If you don't mind, I'll first
answer two questions that you did
not ask, and then address your question on feeding.
First, I
REALLY do not recommend starting a hive with bee packages. Not only they are not acclimated to your climate and have very low disease resistance, but the drones your package-bee hive will produce will be mating with
local queens, undermining the viability of their offspring. So not only your experiences with package
bees will be far from joyful (as you can tell already - they now require feeding, and will need much more care down the road), but by bringing in non-local bees you help destroy what remains of the local wild honeybee population. Catching a local swarm is a far better alternative in most places, except in those where beekeepers have been bringing in so many packages and queens that no local genetics remains! Package bees are NOT compatible with treatment-free beekeeping. Natural beekeeping authorities starting from Georges
de Layens (author of
Keeping Bees in Horizontal Hives) and all the way to Fedor Lazutin (see
Keeping Bees with a Smile) and Kirk Webster (see his chapter in
Raising Honeybee Queens) have been saying that #1 condition for success in natural beekeeping is working with local honeybees only. By the way, for those starting with packages and nucs, Lazutin has been recommending to induce your colony to swarm as soon as possible (by limiting the hive volume so they become congested). This way the new queen will mate with local drones and her offspring will already be "more local" than from the original queen. Killing the original queen once the colony is well established and has plentiful brood (including open brood and eggs, from which they will raise a new queen) is another alternative to make you hive more local and increase their chances of survival.
Second, you will find that a top-bar hive is more difficult to manage successfully for a beginner beekeeper than a horizontal hive with removable frames. The top-bar hive was developed for use in tropical climates with no winter and with plentiful honeyflows almost year around (and for beekeepers accustomed to handling frameless hives). In other climates, its lack of insulation, the elongated shape, and the relatively small size of comb creates problems with successful wintering, overheating, ventilation, uncontrolled swarming, etc. - in addition to higher chance of cross-coming and comb collapses. You CAN keep bees successfully in top-bar hives, but it is just not as hands-off as a horizontal hive with frames such as the Layens (which is the most popular horizontal hive in the world with 150 years of successful use in temperate climates).
As to your original question, you do need to feed your package if you want the bees to survive, and 1:1 sugar:
water (by weight) feed is safer than honey (which may carry the spores of foulbrood unless you have a way to tell that it is guaranteed to come from a foulbrood-free source). Take all precautions against robbing (reduce the size of the entrance; give the feed late in the evening - and only as much as they will consume overnight, etc - see the Layens book for details). How long to feed depends on the weather and natural nectar availability. If the weather is nice and lots of flowers are in bloom, a week or 10 days
should be more than
enough. Many beekeepers, though, feed their bees sugar any time when there's no nectar. By the way, some of the sugar you feed them will end up in honey - be aware of that. This is one of the reasons I never feed my bees sugar, but, then, I never bought any bees either.
Since you got commercial bees, I recommend that you familiarize yourself with best practices for conventional hive management.
The Beekeeper's Handbook by Sammataro and Avitabile is a good guide; and
ABC & XYZ of Bee Culture or
The Hive and the Honey Bee are good references. On top bar hives, specifically, the most comprehensive resource is
Top-Bar Hive Beekeeping by W.A. Mangum.