I am looking for transport from the border crossing at Hussein bridge to Tel Aviv.
The most important factor is price.
But, it's somewhat complicated because the bus that goes to Beit She'an doesn't stop at the border crossing. So the best way to know what bus you need is Google Maps, search for "צומת נהר הירדן" you can use this link. Once you get to Beit She'an you can take a bus to Tel Aviv, I recommend using Google Maps for this as well. There is bus line 845 directly from Beit She'an to Tel Aviv or you would need to take a bus to Afula (411) and from there there are buses to Tel Aviv (825), and other routes according to the time of departure.
Few important notes:
The border crossing is open on Saturday, however there is no public transportation on Saturday in Israel, so if you plan to come on a Saturday, you would have to take a taxi, which would be very expensive.
The same goes for Friday, public transportation works only half a day on Fridays and some lines have different schedules on Fridays while some aren't active at all, so take that into consideration as well.
Line 16 has only 6 buses a day, which means that you might have to wait for a long time for a bus. The bus station is located only 6.6 km (according to Google maps) from the Beit She'an central bus station, so it may be acceptable to take a taxi for this short trip, and then use public transportation from there. All according to your preferences and circumstances.
If you want other options other then Google maps, you can use www.bus.co.il which is an aggregator of all the bus companies, here is an example of how to get from the border crossing to Tel Aviv leaving at 8:00 on February 29th, 2016.
A somewhat related side note:
I personally use only Google Maps to find buses and trains, as I find it more comfortable, faster and more informative that using the sites of the actual bus companies. So I highly recommend using it during your visit whenever the need for public transportation arises, especially when in a new place as the map will not only tell you the time, but also the location of the stations and will guide you to them.
I'm not affiliated with Google in any shape or form, I'm simply sharing my real life experience,
For Israel public transit, http://www.bus.co.il/ is invaluable. I found Google Maps unusable in Israel without knowing Hebrew. This bus website works well even if you only speak English and integrates Google maps. Here's how you'd do your request, first click the marker:
then drop a pin on the popup map:
Click through for connections then more connections to get:
And the more details link next to each itinerary (some are repeated) will include everything you need to know.