how to get back to the bubble form beagle point

You have a few options, but unfortunately, I'm not sure if there's any option that will really meet your criteria. A few of these options you have almost no control over.

See if any of the Fleet Carriers at Beagle Point and nearby systems sell ships

If any carriers near you are selling ships, you could buy one to sacrifice for a free ride back to the bubble. Unfortunately, this will mean that the ship you're currently in will be stuck on a carrier at Beagle Point. You could transfer it back to a station in the bubble, but I would expect that to take a lot of time and a lot more credits - far more than what it cost you to buy originally. You seem intent on keeping your ship if you can, so I'm not sure if this is a good option. But, it is an option.

Find a Fleet Carrier owner moving back to the bubble

Beagle Point is a "famous" destination for pilots to visit. It is entirely likely that carriers will come and go from there. Go into Open and see if there is anyone planning a trip back to colonized space. There are some Discord/forum/Reddit communities and other places on the internet where carrier owners will post departure/destination plans that you could check out too. This will probably be time consuming since carriers actually travel slower than most regular ship fitments. A carrier can travel 500 LY roughly every 20 minutes, which is equivalent to a 25 LY ship that jumps every minute. Any long-distance ship should be able to jump more than 25 LY every minute, with even slightly engineered exploration ships capable of jumping more than twice that distance.

Find a Fleet Carrier owner that is going to decommission their Carrier

The reason Beagle Point is "famous", as you point out, is because of how far it is from Sol. Because it is so far away, it is conceivable that some carrier owners might arrive at Beagle Point, but find the idea of navigating their carrier back home to be a daunting task. If you were on, or last docked on, a carrier which has been decommissioned, then your (re)spawn point no longer exists. Any pilots/ships/modules that were last on a decommissioned carrier will re-appear at the closest station with carrier administration services. For Beagle Point, that should be Colonia. Fun fact: Colonia is a whole lot closer to Sol than Beagle Point, and then you can find another Carrier to hitch a ride on or simply make the trip yourself the rest of the way to the bubble. Do note, however, that decommissioning a carrier takes 7 days to complete and most of the services that it would normally offer will be disabled.

Fly yourself home

You point out that you don't really want to do this, but this is, unfortunately, the only choice you have complete control over while keeping your ship. It is, without a doubt, a time sink and a grind, although your ship fit could mitigate some of the time you end up spending jumping across the galaxy. Hopefully, you're in a solid exploration ship with a 60+ LY jump range and fitted with at least one AMFU (Auto Field-Maintenance Unit). With this setup, you can use neutron stars to boost your jump range and shorten the amount of time spent on your trip back home. Using the spansh neutron plotter is a common tool for pilots who need to plot long routes, and they've recently released an updated version called the galaxy plotter which takes into account your ship build and fuel scooping requirements while plotting the most efficient route through known systems. You could also try to make it more interesting and find some unexplored pockets of the galaxy on your way home and tag your pilot's name to those first discoveries when you finally reach a station.

Self-destruct and replace your ship

You also point out that you don't want to do this. Perhaps you find your ship difficult to replace, or are sentimental about it. I can't really know for sure. But honestly, this is, easily, the fastest option available to you. And not just in when you appear back in the bubble (which would be instantly), but also accounting for recovering your ship. Credits in Elite Dangerous are really, really easy to get. Depending on your mining ship, an evening of mining can net you hundreds of millions or even over a billion credits. There are various Discord communities around that have adhoc mining wings form pretty regularly, so it should be fairly straightforward to find some people to do some mining with and keep it an interesting evening. And you don't need an Anaconda to mine with, a Cobra Mk3 or even an Adder is just fine if that's what you can afford.

In reality, the limiting resource for ship builds is engineering materials. Acquiring engineering materials is much more time consuming than earning credits. But even then, I would expect you to be able to completely replace your ship, whatever it might be, within a few days. And if the ship you are replacing is un-engineered, then this isn't a concern at all. In either case, this is easily the least time consuming option available to you.